Monocentric lens designs and associated imaging systems having wide field of view and high resolution

ABSTRACT

Methods, systems, and devices are disclosed for capturing and forming large high quality images using monocentric optical imaging. In one aspect, an optical imaging system includes an optical imaging module that collects light to form an image on an imaging surface, one or more imaging sensors each including an array of optical detectors located away from the imaging surface to receive light representing the image initially formed on the imaging surface and to convert the received light into detector signals, and optical waveguides coupled between the imaging surface and the one or more imaging sensors to receive light from the imaging surface and configured to selectively deliver a desired portion of the received light to the one or more imaging sensors while suppressing undesired stray light from reaching the one or more imaging sensors so that the optical waveguides effectuate an optical aperture stop with a limited angle range for receiving light by the one or more imaging sensors.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a 35 USC §371 National Stage application ofInternational Application No. PCT/US2013/055892 filed Aug. 20, 2013,which further claims the benefit of priority of U.S. Provisional PatentApplication No. 61/691,234, entitled “MONOCENTRIC LENS DESIGNS ANDASSOCIATED IMAGING SYSTEMS HAVING WIDE FIELD OF VIEW AND HIGHRESOLUTION”, filed on Aug. 21, 2012. The entire content of theaforementioned patent applications are incorporated by reference as partof the disclosure of this application.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

This invention was made with government support under W911NF-11-C-0210awarded by the Army. The government has certain rights in the invention.

TECHNICAL FIELD

This patent document relates to imaging optics including optical lenses,and related imaging systems, devices, methods and materials.

BACKGROUND

Imagers that require the combination of wide field of view, high angularresolution and large light collection present difficult challenges inoptical system design. For example, geometric lens aberrations increasewith aperture diameter, numerical aperture and field of view, and scalelinearly with focal length. This means that for a sufficiently shortfocal length, it is possible to find near diffraction-limited wide anglelens designs, including lenses mass-produced for cellphone imagers.However, obtaining high angular resolution (for a fixed sensor pixelpitch) requires a long focal length for magnification, as well as alarge numerical aperture to maintain resolution and image brightness.This combination is difficult to provide over a wide angle range.Conventional lens designs for longer focal length wide-angle lensesrepresent a tradeoff between competing factors of light collection,volume, and angular resolution. For example, conventionalreverse-telephoto and “fisheye” lenses provide extremely limited lightcollection compared to their large clear aperture and overall volume.However, the problem can go beyond the lens itself. For example, solvingthis lens design only leads to a secondary design constraint, in thatthe total resolution of such wide angle lenses may easily exceed 100Megapixels. This is beyond the current spatial resolution andcommunications bandwidth of a single cost-effective sensor, e.g.,especially for video output at 30 frames per second or more.

SUMMARY

Methods, systems, and devices are disclosed for capturing and forminglarge high quality images using monocentric optical imaging.

In one aspect, an optical imaging system includes a monocentric opticalimaging module including one or more optical elements having concentricsurfaces to collect light and form an image on a curved image surface,one or more optical waveguide bundles each comprising a plurality ofoptical waveguides that are optically coupled to the monocentric opticalimaging module at different locations to receive different portions ofthe collected light at the curved image surface, respectively, eachoptical waveguide being configured to have a tapered waveguide core of across section that varies along the optical waveguide to select desiredcollected light rays to pass through the optical waveguide whilerejecting undesired collected light rays from being transmitted to anoutput facet of the optical waveguide, and one or more imaging sensorsto receive output light from the one or more optical waveguide bundlesand to detect the received output light, the one or more imaging sensorsconfigured to produce a representation of the image on the curved imagesurface of the monocentric optical imaging module.

In another aspect, an optical imaging system includes a monocentricoptical imaging module including one or more optical elements havingconcentric surfaces to collect light and form an image on a curved imagesurface, one or more optical waveguide bundles each comprising aplurality of optical waveguides that are optically coupled to themonocentric optical imaging module at different locations to receivedifferent portions of the collected light at the curved image surface,respectively, in which each optical waveguide bundle includes an inputoptical waveguide bundle facet to receive light from the curved imagesurface and an output optical waveguide facet to output light, one ormore imaging sensors to receive light from the one or more opticalwaveguide bundles and to detect the received light, the one or moreimaging sensors configured to produce a representation of the image onthe curved image surface of the monocentric optical imaging module, anda textured surface structure over the input optical waveguide facetassociated with optical waveguides of each optical waveguide bundle toenhance optical coupling from the curved imaging surface into theoptical waveguides.

In another aspect, an optical imaging system includes an optical imagingmodule that collects light to form an image on an imaging surface, oneor more imaging sensors each including an array of optical detectorslocated away from the imaging surface to receive light representing theimage initially formed on the imaging surface and to convert thereceived light into detector signals, and optical waveguides coupledbetween the imaging surface and the one or more imaging sensors toreceive light from the imaging surface and configured to selectivelydeliver a desired portion of the received light to the one or moreimaging sensors while suppressing undesired stray light from reachingthe one or more imaging sensors so that the optical waveguideseffectuate an optical aperture stop with a limited angle range forreceiving light by the one or more imaging sensors.

In another aspect, an optical imaging system includes a monocentricoptical imaging module including one or more optical elements havingconcentric surfaces and a curved imaging surface, the monocentricoptical imaging module configured to collect light to form an image onthe curved imaging surface, one or more imaging sensors each includingan array of optical detectors located away from the curved imagingsurface to receive light from the imaging surface and to convert thereceived light into detector signals, and an actuator coupled to the oneor more optical elements having concentric surfaces and configured toadjust an axial translation position of the one or more optical elementshaving concentric surfaces relative to the curved imaging surface, alongan optical axis from the one or more optical elements having concentricsurfaces to the curved imaging surface, to change focusing of an objectin a first object plane onto the same curved imaging surface to focusingof an object in a second, separate object plane onto the curved imagingsurface, in which the first and second object planes are at differentaxial locations from each other.

In another aspect, a method for optical imaging using a monocentricoptical imaging module includes operating a monocentric optical imagingmodule including one or more optical elements having concentric surfacesto collect light from a scene at a first object plane to be imaged andto form an image of the first object plane on a curved image surfacewhich is part of a spherical surface that is concentric with the one ormore optical elements having concentric surfaces, and, without adjustinga position or curvature of the curved image surface, adjusting an axialtranslation position of the monocentric optical imaging module to changefocusing of an object on the first object plane onto the curved imagingsurface to focusing of an object on a second object plane onto thecurved imaging surface, in which the second object plane is parallel tothe first object plane but is at a different axial location from thefirst object plane.

In another aspect, a method for optical imaging includes operating anoptical imaging module to collect light to form an image on an imagingsurface, using one or more imaging sensors each including an array ofoptical detectors located away from the imaging surface to receive lightrepresenting the image formed on the imaging surface and to convert thereceived light into detector signals, and using optical waveguidescoupled between the imaging surface and the one or more imaging sensorsto receive light from the imaging surface of the optical imaging moduleto select a desired portion of the received light to reach the one ormore imaging sensors while suppressing undesired stray light fromreaching the one or more imaging sensors so that the optical waveguideseffectuate an optical aperture stop with a limited angle range forreceiving light by the one or more imaging sensors.

In another aspect, a method for optical imaging includes operating anoptical imaging module to collect light and to form an image on animaging surface, coupling optical waveguides to the imaging surface toreceive light of the image formed by the optical imaging module anddeliver received light to one or more imaging sensors located away fromthe imaging surface, and providing a textured surface structure near orat the imaging surface to enhance optical coupling of light into inputfacets of the optical waveguides.

In another aspect, a method for fabricating a monoconcentric opticalimaging system includes forming a flat slab of having fibers beingparallel to one another and perpendicular to the flat slab surfaces,bonding the flat slab onto a flat surface of a wafer to form a bondedstructure, processing an exposed surface of the flat slab bonded ontothe wafer to form spherical surface depressions at different locations,and engaging monocentric optical imaging modules to the sphericalsurface depressions, respectively, so that each spherical surfacedepression serves as a curved imaging surface for forming images by acorresponding monocentric optical imaging module.

In another aspect, an optical imaging system includes a substrate, aflat slab bonded over the substrate, the flat slab having fibers beingparallel to one another and perpendicular to the flat slab surfaces andconfigured to include spherical surface depressions at differentlocations on top of the flat slab, and monocentric optical imagingmodules engaged to the spherical surface depressions, respectively, sothat each spherical surface depression serves as a curved imagingsurface for forming images by a corresponding monocentric opticalimaging module.

In another aspect, an optical imaging system includes a monocentricoptical imaging module having concentric optical surfaces that collectlight in a photographic visible spectrum to form an image on a curvedimaging surface that is concentric with the concentric optical surfacesof the monocentric optical imaging module, in which the monocentricoptical imaging module includes an inner glass ball lens of a spherehaving a low index and an outer glass lens element of a high indexglass, one or more imaging sensors each including an array of opticaldetectors located away from the imaging surface to receive lightrepresenting the image initially formed on the curved imaging surfaceand to convert the received light into detector signals, and opticalwaveguides coupled between the imaging surface and the one or moreimaging sensors to receive light from the curved imaging surface anddeliver the received light to the one or more imaging sensors.

In another aspect, a method for designing a monocentric optical imagingmodule having concentric optical surfaces that collect light to form animage on a curved imaging surface that is concentric with the concentricoptical surfaces of the monocentric optical imaging module, in which themonocentric optical imaging module includes an inner glass ball lens ofa sphere having a low index and an outer glass lens element of a highindex glass, in which the method includes: determining surface radii ofthe inner glass ball and outer glass lens element to minimize 3rd orderSeidel spherical and axial chromatic aberrations for combinations ofglass materials for the inner glass ball and outer glass lens element;optimizing lens prescriptions of the inner glass ball and outer glasslens element via ray tracing of multiple ray heights for a centralwavelength within the photographic visible spectrum to generate lensdesign candidates based on the combinations of glass materials for theinner glass ball and outer glass lens element; computing a polychromaticmean RMS wavefront deformation to generate a ranked list of lens designcandidates for the combinations of glass materials for the inner glassball and outer glass lens element; and confirming the ranked order bycomparing polychromatic diffraction modulation transfer function (MTF)curves of the lens design candidates.

In another aspect, an optical imaging system includes a monocentricoptical imaging module having concentric optical surfaces that collectlight in a photographic visible spectrum to form an image on a curvedimaging surface that is concentric with the concentric optical surfacesof the monocentric optical imaging module, in which the monocentricoptical imaging module includes an inner glass ball lens of a spherehaving a low refractive index of K-GFK68, K-GFK60 or S-FPM2 and threeouter glass lens elements of higher refractive indices; one or moreimaging sensors each including an array of optical detectors locatedaway from the imaging surface to receive light representing the imageinitially formed on the curved imaging surface and to convert thereceived light into detector signals; and optical waveguides coupledbetween the imaging surface and the one or more imaging sensors toreceive light from the curved imaging surface and deliver the receivedlight to the one or more imaging sensors.

In another aspect, an optical imaging system includes a monocentricoptical imaging module having concentric optical surfaces that collectlight in a water transmission spectrum band from 0.38 to 0.55micrometers to form an image on a curved imaging surface that isconcentric with the concentric optical surfaces of the monocentricoptical imaging module, in which the monocentric optical imaging moduleincludes an inner glass ball lens of a sphere having a low refractiveindex and three outer glass lens elements of higher refractive indices,one or more imaging sensors each including an array of optical detectorslocated away from the imaging surface to receive light representing theimage initially formed on the curved imaging surface and to convert thereceived light into detector signals, and optical waveguides coupledbetween the imaging surface and the one or more imaging sensors toreceive light from the curved imaging surface and deliver the receivedlight to the one or more imaging sensors.

In another aspect, an optical imaging system includes a monocentricoptical imaging module having concentric optical surfaces that collectlight in a transmission spectrum band from infrared 0.9 to 1.5 micronsto form an image on a curved imaging surface that is concentric with theconcentric optical surfaces of the monocentric optical imaging module,in which the monocentric optical imaging module includes an inner glassball lens of a sphere having a low refractive index and three outerglass lens elements of higher refractive indices; one or more imagingsensors each including an array of optical detectors located away fromthe imaging surface to receive light representing the image initiallyformed on the curved imaging surface and to convert the received lightinto detector signals; and optical waveguides coupled between theimaging surface and the one or more imaging sensors to receive lightfrom the curved imaging surface and deliver the received light to theone or more imaging sensors.

In another aspect, a method for designing a monocentric optical imagingmodule having concentric optical surfaces that collect light to form animage on a curved imaging surface that is concentric with the concentricoptical surfaces of the monocentric optical imaging module, in which themonocentric optical imaging module includes an inner glass ball lens ofa sphere having a low index and three outer glass lens elements ofhigher refractive indices, in which the method includes: determiningsurface radii of the inner glass ball and three outer glass lenselements for combinations of glass materials for the inner glass balland the three outer glass lens elements to minimize monochromatic andchromatic aberrations; the local optimization method will come somewhereinside the thin pancake shaped area of low criterion value solutions,then at a second step optimization search will follow over the mainravine of the cost function which direction was determined from theminimal absolute Eigen vector of the Hesse matrix at the initial minimumcost function point and locating with number of local optimizations thepoints over this ravine inside pancake shaped area of low value of costfunction; then, at a third step, locating minimums over secondaryravines originated from the primary ravine of cost function with thesame method of traveling over directions of secondary eigen vectors ofthe points over primary ravine with the local optimizations from thesepoints. By investigating the pancake area of low cost function valuewith the square net of ravines the method reliably located the area oflowers cost function value and find location absolute minimum for eachparticular glasses combination.

The subject matter described in this patent document can be implementedin specific ways that provide one or more of the following features. Forexample, in some exemplary embodiments, the present technology includescompact high resolution imager systems and devices operating in visible,NIR, SWIR, MWIR, and LWIR spectrum bands to capture and form images withhigh pixels count (e.g., more than 60 Megapixels) and be able to operateat a rapid frame rate (e.g., 30 frames per second or better). Forexample, the real-time readout ability can be achieved by using themulti-scale architecture with a number of synchronously operatingreceivers each of them having a moderate pixels count in the range of 5Megapixels. The imaging optics can include several types ofsubstantially monocentric or semi-monocentric lenses, which have beendesigned with a unique systematic approach to achieve the optimum F# andimage quality considering operating waveband requirements. For example,the image is formed at the intermediate spherical image surface anddelivered to the number of receivers by fiber bundles or tapers. Withthe use of high numerical aperture high resolution fiber bundles, theconventional physical aperture stop at the center of a monocentric (MC)lens provides light filtering. For example, in the exemplary case ofobservation of a flat Lambertian object, the reduction of imageillumination can be configured to be proportional to the 1/cos3(α),where a is the field angle. The power three is constructed from cosinereduction of input aperture due to the pupil projection on the directionof the fields and cosine in power two reduction of the brightness of thesource due to the cosine reduction of the projection of emitting areaand reduction of the intensity of the source. For example, in theexemplary case of general landscape imaging, the reduction of imageillumination can be as low as 1/cos(α) just due to the reduction of theentrance pupil size at the field points. If an exemplary monocentricimager operates with light filtering providing by the exemplary taperedfiber configuration, the entrance pupil may not contract over the field,and for the case of general landscape observation, there may be no imageillumination reduction at all. This is a beneficial advantage of theexemplary monocentric imagers with a “virtual” aperture stop, e.g., ascompared to conventional imagers. For example, the disclosed monocentriclenses can be used in several exemplary applications including compactsuper-resolution omnidirectional photonic masts, persistentsuper-resolution surveillance cameras, high light collection underwaterimagers, wearable direct bullet impact warning systems, compact foveatedunmanned aerial vehicles that can be capable of real-time downloads withhigh resolution images, e.g., by using restricted band communicationchannel and others.

These and other aspects and their implementations are described ingreater detail in the drawings, the description and the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A shows an optical layout diagram of an exemplary Gigapixelmonocentric imaging system.

FIG. 1B shows an optical layout diagram of an exemplary multi-scalemonocentric-based imaging system with primary and secondary opticsmodules for delivery of intermediate images to an array of receiversusing an waveguide optical fiber delivery system.

FIGS. 2A and 2B show diagrams depicting monocentric lens imaging with aphysical aperture stop at the center of the objective lens, and a“virtual” stop accomplished by limiting the numerical aperture of theimage transfer which, as drawn, are non-imaging optical fibers.

FIG. 3 shows a diagram of an exemplary optical fiber depicting lightfiltering in the straight fibers having numerical aperture less than 1.

FIG. 4A shows a diagrams of exemplary optical fibers depicting rayfiltering in straight and tapered fibers.

FIG. 4B shows a diagram of an exemplary optical fiber depicting lightfiltering in an exemplary ‘hourglass’ double-tapered optical fiberconfiguration, e.g., having the same input-output divergence.

FIG. 5A shows an illustrative process diagram of an exemplaryfabrication method to produce an ‘hourglass’ double-tapered opticalfiber of the disclosed technology.

FIG. 5B shows an illustrative process diagram of an exemplaryfabrication method to produce a curved fiber bundle from half of anexemplary tapered fiber bundle.

FIG. 5C shows exemplary diagrams depicting light filtering into lightguided CMOS pixels, modified to introduce absorption of stray light.

FIGS. 6-8 show illustrative process diagrams of wafer scale fabricationtechniques to produce straight fiber bundles.

FIGS. 8B and 8C show schematic diagrams of exemplary tools to create andshape surface relief patterns for improved fiber coupling.

FIG. 9 shows a diagram of an exemplary imaging system including amonocentric lens with curved fiber bundle image delivery system andcolor CMOS array having pixels pitch two times less than fiber diameterat the output.

FIG. 10 shows diagrams of exemplary “fish-shaped” fiber bundles forlight guiding and stray light filtering.

FIG. 11 shows a diagram depicting the ray output resulting fromilluminating a straight fiber bundle with a concave input face, e.g.,indicating a large variation in output light divergence.

FIG. 12 shows a diagram depicting the coupling efficiency and outputdivergence for the exemplary straight optical fibers of an exemplarymonocentric optical imaging system located at the center field and twooff-axis field points.

FIG. 13 shows a diagram depicting a more detailed view of the exemplaryray-tracing of FIG. 12 through the exemplary straight fibers of theexemplary monocentric optical imaging system.

FIG. 14 shows a diagram depicting the output of an exemplary opticalfiber of an exemplary monocentric optical imaging system located at thecorner field point.

FIG. 15 shows a diagram depicting the detected focal plane signal, e.g.,showing the adjacent pixel crosstalk resulting from the same three fieldpoints.

FIG. 16 shows a diagram depicting the uniform output divergence of anexemplary curved tapered fiber bundle operating with an exemplarymonocentric lens so the principal rays of the lens substantially alignwith the fiber axis at input.

FIG. 17 shows a diagram depicting light coupling into and out of anexemplary straight fiber bundle with a concave input face havingbeam-deflecting features.

FIG. 18 shows a diagram of a magnified view of the exemplary straightfiber bundle in the diagram of FIG. 17, e.g., showing the variation inspatial features of an exemplary structure for input light angledeflection.

FIG. 19 shows a diagram of an exemplary imaging system including anextremely wide field monocentric lens operating in a “virtual” iris modeand including substantially uniform transmission as a function ofillumination angle.

FIG. 20A shows a diagram depicting first and third order considerationsof monocentric lens refocus.

FIG. 20B shows a schematic diagram of an exemplary monocentricmicro-scale imager device capable of focusing using an axial translationmotion.

FIG. 21 shows a diagram depicting third order aberration theory appliedto monocentric lens design.

FIG. 22 shows a diagram depicting monocentric lens real ray tracevariables.

FIG. 23 shows an exemplary plot showing dependence of criterion Q on theradius r₁.

FIG. 24 shows a diagram depicting image formation in an exemplarymonocentric lens.

FIGS. 25A and 25B show diagrams of exemplary lens and global optimumsolutions.

FIGS. 26A and 26B show exemplary data plots depicting modulationtransfer function (MTF) and ray aberrations performance comparisons ofexemplary imaging systems of the disclosed technology.

FIG. 27 shows an exemplary data plot depicting the correlation betweenpolychromatic mean square wavefront deformation and MTF @ 200 lp/mm.

FIG. 28 shows an exemplary diagram and corresponding data plots showingan exemplary highest ranked design solution (e.g., high index centerglass).

FIGS. 29A and 29B show exemplary data plots depicting the MTFperformance of monocentric lens focused at infinity (design) andrefocused at flat object at 0.5 m, respectively.

FIGS. 30A and 30B show an exemplary diagram and data plots of theexemplary top member of the third family (e.g., lower center glassindex) operating in the physical aperture stop, e.g., including a 73°field angle illustrating the effect of aperture vignetting and “virtual”aperture stop mode, with uniform response up to 80°.

FIG. 31 shows exemplary diagrams illustrating a comparison of twoconventional wide field lenses with exemplary monocentric-waveguidelenses, e.g., in which all imagers have a 12 mm focal length, 120° fieldof view, and similar light collection.

FIG. 32 shows an exemplary systematic diagram of photographic lens setupfamilies, including monocentric multi-scale and waveguide imagers.

FIG. 33 shows a cross section of a diagram showing an exemplary compactimager in which the outer lens element is made of molded plastic andincorporates mechanical supports as well as portions of anelectromagnetic focus actuation mechanism.

FIG. 34 shows a diagram of an exemplary compact monocentric lens withneutral spherical Alvarez lens aberration compensator, positioned toprovide no optical power.

FIG. 35 shows a diagram of an exemplary compact monocentric lens withactive spherical Alvarez lens aberration compensator, positioned toprovide optical power.

FIG. 36 shows a diagram of an exemplary MWIR two glass monocentric lens.

FIG. 37 shows an exemplary data plot depicting the MTF of the exemplaryMWIR two glass monocentric lens.

FIG. 38 shows an architectural diagram of an exemplary four glasssemi-monocentric lens.

FIG. 39 shows a data plot showing typical trajectories of exemplaryoptimization methods.

FIG. 40 shows a two dimensional graph of an exemplary four glassmonocentric lens optimization criterion.

FIG. 41 shows a three dimensional countur chart of the exemplary fourglass monocentric lens optimization in the R1-R6 section of theoptimization space.

FIG. 42 shows an optical layout diagram of an exemplary four glasssemi-monocentric lens which operates in the extended waveband of 400 to1000 nm.

FIG. 43 shows a data plot of the MTF of an exemplary four glassmonocentric lens operating in the extended waveband of 400 to 1000 nmwith uniform sensitivity of the sensor.

FIG. 44 shows a data plot of the MTF of an exemplary four glassmonocentric lens which operates without any band pass filters with thefront illuminated CCDs.

FIG. 45 shows a data plot of the MTF of an exemplary four glassmonocentric lens which operates with the back illuminated CCDs.

FIG. 46 shows an optical layout diagram of an exemplary four glasssemi-monocentric lens which operates with the back illuminated CCDs.

FIG. 47 shows a data plot of the MTF performance of an exemplarymonocentric underwater lens.

FIG. 48 shows a data plot of the MTF performance of an exemplarymonocentric near infrared lens.

FIG. 49 shows an optical layout diagram of an exemplary monocentric SWIRlens.

DETAILED DESCRIPTION

Monocentric lenses can be used to form imaging devices or systems forvarious imaging applications, including panoramic high-resolutionimagers, where the spherical image surface is directly detected bycurved image sensors or optically transferred onto multiple conventionalflat focal planes.

Wide-angle imaging based on monocentric lenses can be achieved by usinghemispherical or spherical optical surfaces which share a single centerof curvature. This symmetry yields zero coma or astigmatism over ahemispherical image surface, and on that surface provides a field ofview limited only by vignetting from the central aperture stop. Thechallenge of using a curved image surface limited the practicalapplication of this type of lens, but there has been a resurgence ofinterest in monocentric lens imaging. In some systems, anomnidirectional imager uses a spherical ball lens contained within aspherical detector shell. In another system, for example, a monocentriclens is used as the objective in a multi-scale imager system, whereoverlapping regions of the spherical image surface are relayed ontoconventional image sensors, and where the mosaic of sub-images can bedigitally processed to form a single aggregate image. In a similarexample, a system includes a closely related configuration using a glassball and single element relay lenses, recording and digitally combiningoverlapping images from multiple adjacent (e.g., five adjacent) imagesensors.

Monocentric lenses and spherical image formation provides favorablescaling to long focal lengths, and have been shown capable of two ordersof magnitude higher space-bandwidth product (e.g., number of resolvablespots) than conventional flat field systems of the same physical volume.For example, in early monocentric lens cameras, the usable field of viewwas limited by the vignetting and diffraction from the central lensaperture, as well as the ability of recording media to conform to aspherical image surface. However, the system aperture stop need not belocated in the monocentric lens. For example, an exemplary design of amulti-scale monocentric lens can include locating the aperture stopwithin the secondary (relay) imagers can enable uniform relativeillumination and resolution over the full field. Such exemplary designsmaintain F/2.4 light collection with near-diffraction limited resolutionover a 120° field of view. For example, with 1.4 micron pitch sensors,this can yield an aggregate resolution of 2.4 Gigapixels.

An example of a Gigapixel monocentric imaging system is shown incross-sectional optical layout diagram of FIG. 1A, which shows amonocentric multi-scale imager 101 that integrates a 2-dimensionalmosaic of sub-images. The monocentric imager 101 includes amonocentricprimary lens system 101 a that inputs light from various field angles,e.g., over 120° field of view (FOV). The monocentric primary lens system101 a transfers the light to be received by a spherical image surface104, from which the light is relayed via image relay optics 103 toindividual focal planes which can include a plurality of imaging sensors105, e.g., CMOS sensors or other imaging sensors, e.g., including butnot limited to flat CCD, FPA receivers, or others. Some other examplesof monocentric lens imaging systems are provided in U.S. patentapplication 13/437,907, entitled “MONOCENTRIC IMAGING,” filed Apr. 2,2012, of which the entire contents are incorporated by reference for allpurposes as part of the disclosure of this patent document.

FIG. 1B shows a monocentric imaging system for imaging wide and uniformfields by using optical waveguides. The monocentric imaging system 102includes a monocentric primary optical imaging module 102 a to collectlight from various field angles, e.g., over 120° FOV. In this example,instead of relay optics, the monocentric imaging system 102 includes aspherical image surface 108 to transfer the collected light to planarimage sensors 107 using one or more multimode fiber bundles 106. Forexample, the image sensors 107 can include CMOS-based image sensors orother imaging sensors, e.g., including but not limited to flat CCD, FPAreceivers, among others. For example, fused fiber faceplates can beconfigured with high spatial resolutions and light collection (e.g., 2.5microns between fiber cores, and numerical aperture of 1), and can beconfigured as straight or tapered. For example, straight fiber bundlescan project sufficiently far to allow space for the packaging ofexemplary CMOS image sensors 107. Alternatively, for example, themultimode optical fiber bundles 106 can be configured as tapered opticalfiber bundles, e.g., which can provide 3:1 demagnification used in therelay optics, as shown in FIG. 1B. The monocentric imaging system 102includes a microprocessor 109 coupled to the imaging sensors 107 tocombine individual images from the imaging sensors 107 into a singlecomposite image representing the image on the spherical image surface108.

In some examples, fiber bundles may introduce artifacts from multiplesampling of the image, which can be mitigated through post-detectionimage processing. In addition, the edges between adjacent fiber bundlescan introduce “seams” in the collected image, whose width depends on theaccuracy of fiber bundle fabrication and assembly. These seams can alsobe mitigated through post-detection image processing. Beneficially, forexample, waveguide transfer can reduce overall physical footprint andsignificantly increase light collection. In addition, the waveguidetransfer can improve light collection efficiency over relay imaging. Insome multi-scale optics structures, for example, light from a particulardirection (field angle) which is close to the intersection of theeadjacent sets of relay optics must be divided between the threeapertures, reducing optical energy and diffraction limited spatialresolution, while the waveguide can transfer all light energy from eachfield angle to a single sensor.

Disclosed are techniques, systems, and devices for imaging andwaveguide-based transfer of the spherical image surface formed by themonocentric lens onto planar image sensors, such that the system inputaperture and resolution are substantially independent of input angle.Also described in this patent document is an aberration analysis thatdemonstrates that wide-field monocentric lenses can be focused by purelyaxial translation, e.g., enabling applications of autofocusing and allin focus imaging techniques. The patent document also presents asystematic design process to identify the best designs for two glasssymmetric monocentric lenses and four glass semi-monocentric lenses.Exemplary implementations of the disclosed systematic design approachare presented herein showing number of exemplary designs, e.g., F/1.7,12 mm focal length imagers with up to 160° field of view, as well assuper compact 3 mm focal length imagers, which compares favorably insize and performance to conventional wide-angle imagers. For example, anumber of imager embodiments for visible, near infrared (NIR),short-wave infrared (SWIR), mid-wave infrared (MWIR), and long wave(LWIR) operations are given, and a number of specific monocentric (MC)lens applications are described. Additionally, for example, a number ofapplications such as omnidirectional super-resolution photonic mast,compact high resolution cell phone cameras, foveated aerial unmannedvehicle imager, among others, are also disclosed.

I. Monocentric Multi-scale Imager's Architecture and Principals ofOperation

Practical implementation of high quality, high-resolution imagingdevices can be challenging. For example, some challenges can beattributed at least in part to the expense associated with manufacturingextremely large area image sensors. For example, a large synaptictelescope, with a 3.2 Gigapixel focal plane, which uses 189, 4K by 4K,10-μm pixel charge-coupled devices (CCDs), with a 9.6-degree field ofview over a 640-mm planar image plane, is estimated to occupy 8 cubicmeters and cost around $105 Million. For example, another challenge canbe associated with aberration scaling of large image plane lenses. Thatis, lens aberrations scale with size such that a lens system (e.g., aCooke triplet) that is diffraction limited at, for example, a focallength of 10 mm can fail when configured to operate at a focal length of100 mm due to aberrations.

One approach for producing very high-resolution (e.g., Gigapixel)imagers is to utilize a multiple macro-camera array configuration, wherea mosaic image can be acquired by a large number of independent cameras.In particular, such a macro-camera array can be arranged to include nindependent diffraction limited cameras, each having a focal plane withS pixels. Each camera can be constructed as part of a cylindricalpackage, where the diameter of the cylinder is the input aperture of thecamera, and each camera can produce an independent sample image of theobject field. In such a macro-camera array, to acquire high resolutionimages, the field of view of each independent camera should have minimaloverlap with the neighboring cameras. In order to enable capturinghigher resolution images using such a macro camera system, the focallengths of the independent cameras must be increased, resulting in anincreased physical volume, weights and the overall cost of the cameraarray. These costs become prohibitive for practical implementation ofvery high resolution imagers (e.g., where images in the range of severalGigapixels are needed).

To reduce the cost and size associated with macro-camera arrays, somesystems utilize a “multi-scale” lens design that includes a commonprimary optics section followed by a multiple secondary section. In suchmulti-scale systems, the primary optics can be curved to minimizeaberrations, and the secondary lenses can each be designed to correctthe off-axis aberration of the primary lens at an associated fieldangle. The multi-scale imagers often produce segmented image planes withoverlapping images that can be digitally processed and stitched togetherto produce a single large image. Such a segmented image plane, however,does not require a massive flat focal plane array and, therefore,facilitates the construction of high-resolution imagers with a smallersize. In addition, such multi-scale configurations provide betterscaling of aberrations for low F-number Gigapixel imagers.

Nevertheless, practical implementation of such multi-scale imagers isstill challenging since the manufacture of free-form (non-rotationallysymmetric) aspheric components associated with the secondary optics isnot trivial. Further, the lenses in the secondary section (i.e.,free-form optical components with no axis of symmetry) must beindividually fabricated and positioned with high degree of accuracy in a3-dimensional space to correct the associated aberration associated witheach field angle. As such, each of the image planes may be oriented at adifferent scale or angle. These and other shortcomings of themulti-scale lens design make it difficult to produce a cost effectiveimaging system that can be physically scaled to Gigapixel resolution.

The disclosed embodiments relate to methods, devices and systems thatcan produce extremely high-resolution images while utilizing opticalcomponents that can be manufactured and implemented feasibly within acompact imaging system. Such imaging systems can be produced at leastin-part by utilizing a primary optics section that is configured toproduce the same off-axis aberrations for all field angles. The primaryoptics section, which provides a common aperture, is radially symmetricand constitutes a monocentric lens. That is, the primary optics sectioncomprises one or more surfaces adapted to form a symmetrical arrangementaround a common point of origin. It should be noted that the term lensis used in this document to include a single lens (or a simple lens), aswell as a compound lens that includes more than one optical element. Insome embodiments, the monocentric lens is comprised of one or morespherical or hemispherical sections with a common center of curvature.Such a monocentric configuration provides a curved image plane andproduces identical or nearly identical aberrations at each field angle.It should be noted that the terms spherical and hemispherical are usedto convey surfaces or sections that are substantially spherical orhemispherical. For example, the geometry of such surfaces or sectionsmay deviate from a perfect sphere or hemisphere due to manufacturinglimitations. Because in such architecture aberrations over the field donot change, the secondary optics can be identical all over the fieldwhich significantly reduce the overall cost of the imager.

The high-resolution imagers of the disclosed embodiments also include asecondary optics section that is configured to correct residual on-axisaberrations of the monocentric primary optics section that is identicalor nearly identical at each field angle. Since the aberrations areon-axis, the secondary optics section can be constructed usingrotationally symmetric components (e.g., aspheres) rather than freeformoptics used in other multi-scale designs. The use of rotationallysymmetric aspheres in the secondary optics section allows usingconvenient fabrication processes such as some well-establishedcommercial fabrication processes, and facilitates construction ofimagers using simple alignment techniques.

The monocentric multi-scale imager 101 includes substantially identicalsecondary optics components 103, as shown in FIG. 1A. While suchsecondary optics include substantially identical objectives, it is stillvery expensive to implement. The monocentric lenses are able to formhigh quality image by themselves. For example, as shown in the exemplaryembodiment of the multi-scale monocentric imaging system 102 of FIG. 1B,the images can be delivered from the sperical image surface 108 to anumber of imaging sensors 107, e.g., CMOS sensors, via low cost opticalfiber bundles 106, e.g., which can be configured as tapered opticalfiber waveguides. This can significantly reduce the overall cost of thesystem.

II. Monocentric Lens with Fibers Image Delivery System

In one aspect, an optical imaging system includes a monocentric opticalimaging module including one or more optical elements having concentricsurfaces to collect light and form an image on a curved image surface,one or more optical waveguide bundles each comprising a plurality ofoptical waveguides that are optically coupled to the monocentric opticalimaging module at different locations to receive different portions ofthe collected light at the curved image surface, respectively, eachoptical waveguide being configured to have a tapered waveguide core of across section that varies along the optical waveguide to select desiredcollected light rays to pass through the optical waveguide whilerejecting undesired collected light rays from being transmitted to anoutput facet of the optical waveguide, and one or more imaging sensorsto receive output light from the one or more optical waveguide bundlesand to detect the received output light, the one or more imaging sensorsconfigured to produce a representation of the image on the curved imagesurface of the monocentric optical imaging module.

Implementations of the optical imaging system can optionally include oneor more of the following exemplary features. For example, each opticalwaveguide can include a waveguide section having a cross section in thetapered waveguide core to decrease along a direction directed from thecurved image surface to a corresponding imaging sensor. For example,each optical waveguide can include a waveguide section having a crosssection in the tapered waveguide core to first decrease along adirection directed from the curved image surface to a correspondingimaging sensor and then to increase along the direction directed fromthe curved image surface to the corresponding imaging sensor. Forexample, the optical waveguides in each optical waveguide bundle can bebent at different bending angles, respectively, at the curved imagesurface of the monocentric optical imaging module. In someimplementations, the optical imaging system can further include atextured surface structure over input facets of the optical waveguidesof each optical waveguide bundle to enhance optical coupling into theoptical waveguides. For example, the textured surface structure caninclude refractive micro prisms. For example, the textured surfacestructure can include a diffraction grating layer. For example, thetextured surface structure can include a locally spatially-varyingoptically patterned layer. For example, the textured surface structurecan include a locally spatially varying optically patterned reflectivelayer. For example, the textured surface structure can include a locallyspatially varying optically patterned refractive layer. For example, thetextured surface structure can include a locally spatially varyingoptically patterned diffractive layer. For example, each opticalwaveguide bundle can be configured to have a tapered exterior profilebetween the monocentric optical imaging module and the one or moreimaging sensors. For example, the optical waveguides in each opticalwaveguide bundle can be configured as optical fibers. For example, theimaging sensors can be planar imaging sensors. For example, each imagingsensor can include a planar array of optical detectors. In someimplementations, for example, the monocentric optical imaging module caninclude a ball lens element formed of a substantially spherical volumeof an isotropic material. In some implementations, for example, themonocentric optical imaging module can include a ball lens elementhaving a first refractive index, and a lens element having a sphericalsurface formed outside the ball lens element to be concentric with theball lens element and having a second refractive index. In someimplementations, for example, the monocentric optical imaging module caninclude a ball lens element formed of a solid sphere having a firstrefractive index, a first lens element having a first spherical surfaceformed outside the ball lens element to be concentric with the ball lenselement and having a second refractive index, and a second lens elementhaving a second spherical surface formed outside the ball lens elementto be concentric with the ball lens element, the second lens elementhaving a third refractive index. For example, the first lens element canbe a hemispherical shell located relative to the ball lens element toreceive input light, and the second lens element can be a hemisphericalshell located relative to the ball lens element to output light towardsthe curved image surface and the array of the optical waveguide bundles.In some implementations, for example, the optical imaging system caninclude a meniscus concentric lens element separated from the ball lensand formed of a material having a fourth refractive index to chromaticcorrection of the image at the curved image surface. For example, themonocentric optical imaging module can include an optical aperture stopthat transmits a restricted portion of light incident on the monocentricimaging module at small incident angles to pass through the monocentricoptical imaging module while blocking light at large incident angles, aball lens element formed of a solid sphere having a first refractiveindex, a first lens element having a first spherical surface formedoutside the ball lens element to be concentric with the ball lenselement and having a second refractive index, and a second lens elementhaving a second spherical surface formed outside the ball lens elementto be concentric with the ball lens element, the second lens elementhaving a third refractive index. For example, the monocentric opticalimaging module includes two or more lenses having concentric sphericalsurfaces. In some implementations, for example, the optical imagingsystem can include an array of the optical waveguide bundles coupled tothe curved imaging surface of the monocentric imaging module atdifferent locations, each optical waveguide bundle of the arraycapturing a part of the image on the curved imaging surface anddifferent optical waveguide bundles capturing different parts of theimage on the curved imaging surface, respectively, an array of theimaging sensors respectively coupled to the different optical waveguidebundles, one imaging sensor per optical waveguide bundle, and a signalprocessing unit coupled to the imaging sensors to combine individualimages from the array of imaging sensors into a single composite imagerepresenting the image on the curved imaging surface of the monocentricimaging module. For example, the signal processing unit can beconfigured to reduce image blurring caused by optical crosstalk of theguided light between adjacent optical waveguides bundles. For example,waveguide input sides of adjacent optical waveguide bundles are disposedwith a minimal spacing so that the image formed on the curved imagesurface is conducted in nearly contiguous regions on to the array of theimaging sensors. In some implementations, for example, the opticalimaging system can further include a lens focusing actuator coupled tothe monocentric optical imaging module to adjust an axial translationposition of the one or more optical elements having concentric surfacesrelative to the curved image surface and the one or more opticalwaveguide bundles to control focusing of the monocentric optical imagingmodule at the curved image surface. For example, the lens focusingactuator can include a voice coil actuator. In some examples, themonocentric optical imaging module can include two optical elementshaving complementary phases to form an Alvarez lens for close focusingoperations.

In another aspect, an optical imaging system includes a monocentricoptical imaging module including one or more optical elements havingconcentric surfaces to collect light and form an image on a curved imagesurface, one or more optical waveguide bundles each comprising aplurality of optical waveguides that are optically coupled to themonocentric optical imaging module at different locations to receivedifferent portions of the collected light at the curved image surface,respectively, in which each optical waveguide bundle includes an inputoptical waveguide bundle facet to receive light from the curved imagesurface and an output optical waveguide facet to output light, one ormore imaging sensors to receive light from the one or more opticalwaveguide bundles and to detect the received light, the one or moreimaging sensors configured to produce a representation of the image onthe curved image surface of the monocentric optical imaging module, anda textured surface structure over the input optical waveguide facetassociated with optical waveguides of each optical waveguide bundle toenhance optical coupling from the curved imaging surface into theoptical waveguides.

Implementations of the optical imaging system can optionally include oneor more of the following exemplary features. For example, the opticalwaveguides in each optical waveguide bundle can include first opticalwaveguide portions that are bent at different bending angles,respectively, at the curved image surface of the monocentric opticalimaging module. For example, the textured surface structure can includea layer of micro prisms. For example, the textured surface structure caninclude a diffraction grating layer. For example, the textured surfacestructure can include a locally spatially varying optically patternedlayer. For example, the textured surface structure can include a locallyspatially varying optically patterned reflective layer. For example, thetextured surface structure can include a locally spatially varyingoptically patterned refractive layer. For example, the textured surfacestructure can include a locally spatially varying optically patterneddiffractive layer. For example, each optical waveguide bundle can beconfigured to have a tapered exterior profile between the monocentricoptical imaging module and a corresponding imaging sensor. For example,each optical waveguide can include a waveguide section having a crosssection in the tapered waveguide core to decrease along a directiondirected from the curved image surface to the one or more imagingsensors. For example, each optical waveguide can include a waveguidesection having a cross section in the tapered waveguide core to firstdecrease along a direction directed from the curved image surface to acorresponding imaging sensor and then to increase along the directiondirected from the curved image surface to the corresponding imagingsensor. In some implementations, for example, the monocentric opticalimaging module can include a ball lens element formed of a solid spherehaving a first refractive index, and a lens element having a sphericalsurface formed outside the ball lens element to be concentric with theball lens element and having a second refractive index. In someimplementations, for example, the monocentric optical imaging module caninclude a ball lens element formed of a solid sphere having a firstrefractive index, a first lens element having a first spherical surfaceformed outside the ball lens element to be concentric with the ball lenselement and having a second refractive index, and a second lens elementhaving a second spherical surface formed outside the ball lens elementto be concentric with the ball lens element, the second lens elementhaving a third refractive index. For example, the first lens element canbe one half spherical shell located relative to the ball lens element toreceive input light, and the second lens element can be one halfspherical shell located relative to the ball lens element to outputlight towards the curved image surface and the array of the opticalwaveguide bundles. In some implementations, for example, the opticalimaging system can further include a spherical lens element formed of amaterial having a fourth refractive index to provide the curved imagesurface. In some examples, the monocentric optical imaging module caninclude an optical aperture stop that transmits a restricted portion oflight incident on the monocentric imaging module at small incidentangles to pass through the monocentric optical imaging module whileblocking light at large incident angles. In some examples, themonocentric optical imaging module can include an optical aperture stopthat transmits a restricted portion of light incident on the monocentricimaging module at small incident angles to pass through the monocentricoptical imaging module while blocking light at large incident angles, aball lens element formed of a solid sphere having a first refractiveindex, a first lens element having a first spherical surface formedoutside the ball lens element to be concentric with the ball lenselement and having a second refractive index, and a second lens elementhaving a second spherical surface formed outside the ball lens elementto be concentric with the ball lens element, the second lens elementhaving a third refractive index. In some examples, the monocentricoptical imaging module can include two or more lenses having concentricspherical surfaces. In some implementations, for example, the opticalimaging system can include an array of the optical waveguide bundlescoupled to the curved imaging surface of the monocentric imaging moduleat different locations, each optical waveguide bundle of the arraycapturing a part of the image on the curved imaging surface anddifferent optical waveguide bundles capturing different parts of theimage on the curved imaging surface, respectively, an array of theimaging sensors respectively coupled to the different optical waveguidebundles, one imaging sensor per optical waveguide bundle, and a signalprocessing unit coupled to the imaging sensors to combine individualimages from the array of imaging sensors into a single composite imagerepresenting the image on the curved imaging surface of the monocentricimaging module. For example, the signal processing unit can beconfigured to reduce image blurring caused by optical crosstalk of theguided light between adjacent optical waveguide bundles. For example,waveguide input sides of adjacent optical waveguide bundles can bedisposed with a minimal spacing so that the image formed on the curvedimage surface is conducted in nearly contiguous regions on to the arrayof the imaging sensors. In some implementations, for example, theoptical imaging system can further include a lens focusing actuatorcoupled to the monocentric optical imaging module to adjust an axialtranslation position of the one or more optical elements havingconcentric surfaces relative to the curved image surface and the one ormore optical waveguide bundles to control focusing of the monocentricoptical imaging module at the curved image surface. For example, thelens focusing actuator can include a voice coil actuator. In someexamples, the monocentric optical imaging module can include two opticalelements that are operable to move relative to each other to provide anadjustable phase profile for compensation of an aberration of themonocentric optical imaging module.

In another aspect, an optical imaging system includes an optical imagingmodule that collects light to form an image on an imaging surface, oneor more imaging sensors each including an array of optical detectorslocated away from the imaging surface to receive light representing theimage initially formed on the imaging surface and to convert thereceived light into detector signals, and optical waveguides coupledbetween the imaging surface and the one or more imaging sensors toreceive light from the imaging surface and configured to selectivelydeliver a desired portion of the received light to the one or moreimaging sensors while suppressing undesired stray light from reachingthe one or more imaging sensors so that the optical waveguideseffectuate an optical aperture stop with a limited angle range forreceiving light by the one or more imaging sensors.

Implementations of the optical imaging system can optionally include oneor more of the following exemplary features. For example, each of theoptical waveguides can include a tapered waveguide section to select thedesired portion of the received light while suppressing the undesiredstray light. For example, the optical imaging module can include amonocentric optical imaging module having concentric optical surfacesand the imaging surface is a curved imaging surface that is concentricwith the concentric optical surfaces of the monocentric optical imagingmodule. In some implementations, for example, the optical imaging systemcan further include a lens focusing actuator coupled to the monocentricoptical imaging module to adjust an axial translation position of atleast one optical element inside the monocentric optical imaging modulerelative to the curved imaging surface to control focusing of themonocentric optical imaging module at the curved imaging surface. Insome implementations, for example, the optical imaging system canfurther include a textured surface structure over input facets of theoptical waveguides to enhance optical coupling from the imaging surfaceinto the optical waveguides. For example, the textured surface structurecan be optically reflective. For example, the textured surface structurecan be optically refractive. For example, the textured surface structurecan be optically diffractive. In some examples, the monocentric opticalimaging module having concentric optical surfaces can include twooptical elements that are operable to move relative to each other toprovide an adjustable phase profile for compensation of an aberration ofthe monocentric optical imaging module.

In another aspect, a method for optical imaging includes operating anoptical imaging module to collect light to form an image on an imagingsurface, using one or more imaging sensors each including an array ofoptical detectors located away from the imaging surface to receive lightrepresenting the image formed on the imaging surface and to convert thereceived light into detector signals, and using optical waveguidescoupled between the imaging surface and the one or more imaging sensorsto receive light from the imaging surface of the optical imaging moduleto select a desired portion of the received light to reach the one ormore imaging sensors while suppressing undesired stray light fromreaching the one or more imaging sensors so that the optical waveguideseffectuate an optical aperture stop with a limited angle range forreceiving light by the one or more imaging sensors.

Implementations of the method for optical imaging can optionally includeone or more of the following exemplary features. For example, eachoptical waveguide can be tapered. For example, the optical imagingmodule can be a monoconcentric optical imaging module having concentricoptical surfaces, and the imaging surface can be part of a sphericalsurface that is concentric with the concentric optical surfaces of themonoconcentric optical imaging module. For example, in someimplementations, the method can include adjusting an axial position ofthe monoconcentric optical imaging module at different positions tofocus objects at different object planes at different axial positions onto the spherical imaging surface. For example, in some implementations,the method can include providing a textured surface structure over inputfacets of the optical waveguides to enhance optical coupling into theoptical waveguides. For example, in some implementations, the method caninclude performing the optical imaging without using an optical aperturestop in an optical path in the optical imaging module and between theoptical imaging module and the imaging surface.

In another aspect, a method for optical imaging includes operating anoptical imaging module to collect light and to form an image on animaging surface, coupling optical waveguides to the imaging surface toreceive light of the image formed by the optical imaging module anddeliver received light to one or more imaging sensors located away fromthe imaging surface, and providing a textured surface structure near orat the imaging surface to enhance optical coupling of light into inputfacets of the optical waveguides.

Implementations of the method for optical imaging can optionally includeone or more of the following exemplary features. For example, theoptical imaging module can be a monoconcentric optical imaging modulehaving concentric optical surfaces and the imaging surface is part of aspherical surface that is concentric with the concentric opticalsurfaces of the monoconcentric optical imaging module. For example, insome implementations, the method can include adjusting an axial positionof the monoconcentric optical imaging module at different positions tofocus objects at different object planes at different axial positions onto the spherical imaging surface. For example, in some implementations,the method can include configuring each optical waveguide to includetapered section to select a desired portion of the received light toreach the one or more imaging sensors while suppressing undesired straylight from reaching the one or more imaging sensors so that the opticalwaveguides effectuate an optical aperture stop with a limited anglerange for receiving light by the one or more imaging sensors.

FIG. 2A shows a diagram of a monocentric lens imaging system 202including a physical aperture stop at the center of the objective lens.In this example, a physical aperture configured at the center of theobjective lens of the system 202 is projected onto the field angle. At60° incidence (e.g., of the exemplary 120° FOV), the aperture iselliptical and reduced in width by 50%, with a corresponding decrease inlight transmission and diffraction-limited resolution.

FIG. 2B shows a diagram of a monocentric lens imaging system 200including a “virtual stop” imagers 201 that limit the numerical apertureof the image transfer which, as exemplified in the diagram of FIG. 2B,can include non-imaging optical fibers 203. For example, the field ofview of the monocentric virtual stop imagers 201 can be configured to beextraordinarily wide. As FIG. 2B shows, moving the aperture stop to thelight transfer enables uniform illumination and resolution over a 160°field of view, where even at extreme angles the input light illuminatesthe back imaging surface of the monocentric objective of the imagingsystem 200. For example, the imaging system 102 as shown in FIG. 1Bindicates that the image transfer optics perform all stray lightcontrol, and does not show non-sequential paths from surfacereflections. In practice, for example, an oversized physical aperture orother light baffles can be used to block most of the stray light, whilethe images transfer optics provide the final, angle-independentapodization. While such practical optomechanical packaging constraintscan limit the practical field of view, the potential for performanceimprovement over a conventional “fisheye” lens is clear.

As shown in FIGS. 2A and 2B, in both imaging systems 202 and 200, straylight can be controlled using a physical aperture stop in the at thecenter of the monocentric lens (system 202 of FIG. 2A), or through thevirtual stop achieved by limiting light transmission in the imagetransfer optics (system 200 of FIG. 2B). In the exemplary case of relayimaging, this can be implemented using a physical aperture stop internalto the relay optics. In the exemplary case of optical fiber waveguidetransfer, this can be implemented by restricting the numerical aperture(NA) of the optical fiber bundles.

FIG. 3 shows a diagram of an exemplary optical fiber 300 depicting lightfiltering in the straight fibers having numerical aperture less than 1.In one example, straight fiber bundles with a lower index differencebetween core and cladding glasses that are currently available typicallyinclude a numerical aperture of 0.28. The diagram of FIG. 3 shows anexample of stray light filtering in an exemplary straight fiber bundleconstructed from the fibers 300 with a restricted numerical apertureare. Rays having incident angles less than θ_(max) will be transferredthrough the fiber. Other rays will be stopped. The sin(θ_(max))=√{squareroot over (n_(core) ²)}−n_(clad) ², where n_(core) is refraction indexof the core and n_(clad) is refraction index of the cladding.

FIG. 4A shows a diagrams of an exemplary straight optical fiber 400 forray filtering and an exemplary tapered optical fiber 401 for rayfiltering. For example, high index contrast bundles with a spatial taperto a smaller output face as shown in the exemplary optical fiber 401 canprovide a controlled NA. Such bundles have the original output NA, butconservation of étendue reduces the input NA of a tapered fiber bundleby approximately the ratio of input to output diameter. For example, a3:1 taper of input to output width with a 1.84 core and 1.48 claddingindex, yields approximately 0.3 input NA.

The principles of light filtering in an exemplary fiber taper were shownin FIG. 4A. For example, if the fiber is tapered the light initiallypropagating with large angle will be stripped inside. This highpropagating angle light stripping is driven by the étendue conservationlaw. The stripping of large angle light, and reduction in effectivenumerical aperture, is a property of fiber bundles. This has beentreated as a limitation (e.g., in using tapered fiber bundles toconcentrate light, there are limits to how much light can beconcentrated). However, in a suitably designed imaging system, andespecially in monocentric lens systems, the lens can be designed so thatundesired stray light (which blurs or washes out the image) is incidentupon the image surface with larger angles than the desired, lowaberration image light. The disclosed technology utilizes this propertyof fiber bundles to advantage. In some implementations of the disclosedtechnology, fiber transmission characteristics and the physical shape ofthe fiber are configured to deliberately discriminate between desiredsignal and noise in the disclosed imaging systems, by selectivelyblocking undesired light from reaching the sensor.

If the fiber is tapered down, the angle of light emitted is larger thanthe original input angle. If a bundle is tapered up (larger output corethan input core diameter), the emitted light has a smaller angle. FIG.4B shows a diagram of an exemplary optical fiber 450 depicting lightfiltering in an exemplary ‘hourglass’ double-tapered optical fiberconfiguration, e.g., having the same input-output divergence. In thisexample, the fiber 450 is tapered down, and then tapered up to the samecore diameter, which will cause the larger incident rays to be strippedmidway through, but the light emitted from the re-enlarged aperture willreturn to the incident ray angle.

Such an exemplary hourglass shape can be configured using disclosedfabrication processes described herein for tapered fiber bundles. Forexample, the net effect of an hourglass fiber bundle is a fiber bundlewhose input aperture active area (and light transfer efficiency) islarge, but whose input numerical aperture is smaller than would beexpected for the index contrast between core and cladding. Thisexemplary configuration can provide the transfer function needed toprovide a “virtual iris” in the monocentric (or other shape) imager,e.g., such as the exemplary monocentric imager 200 shown in FIG. 2B. Insome examples, the hourglass structure can also be configured to beasymmetric, e.g., with a net magnification or demagnification, asdesired. The disclosed technology can use the exemplary dual-taperedfiber bundle to impose stray light stripping and independently controlthe light emission angle from the exit face of the fiber, for optimalimage sensing.

FIG. 5A shows an illustrative process diagram of an exemplaryfabrication method to produce an ‘hourglass’ double-tapered opticalfiber of the disclosed technology. The example shown in FIG. 5A includesa three step process to taper a fiber bundle in the exemplary hourglassconfiguration. The exemplary fabrication method can include a process tomount a plurality of straight optical fibers 502 to “cold tip” fixtures501. After mounting the bundle in the “cold tip” fixtures 501, theexemplary fabrication method can include a process to stretch the fiberbundles with heat applied to the center region of the fiber bundles 502,e.g., until glass reaches glass transition temperature, in which theends are held in heat sinks that remain cool and do not deform, formingan hourglass-shaped optical fiber bundle 503. In some implementations,for example, the exemplary fabrication method can include a process tocut and polish the hourglass-shaped optical fiber bundles 503 into twotaper fiber bundles 504.

The disclosed technology can include an optical fiber bundle structuredto include optical fibers that curve from a spherical image inputsurface towards a flat output surface with no change in fiber diameter.For example, light which is optically coupled into the fiber bundle fromthe concave side is guided around the bend to the output on the flatside with little or no loss. Fiber bends do not introduce losses likefiber tapers, as the light propagating in a gently curved fiber has nonet angle change. This kind of fully 3-dimensional shape can bedifficult to fabricate. FIG. 5B shows an illustrative process diagram ofan exemplary fabrication method of the disclosed technology to produce acurved fiber bundle from half of a tapered fiber bundle. For example, atapered fiber bundle, e.g., such as the tapered fiber bundle 504, can bepolished with a spherical curvature on one face 551 to form a curvedoptical fiber bundle 555, so that the fibers are substantially pointedtowards a common center. As shown in FIG. 5B, the tapered fiber bundle504 can be polished such that the fiber bundle is of a desired size, asshown by the exemplary curved (conforming cup) fiber bundle 555 a and555 b. This may not be exactly spherical, since the fiber cannot bedrawn to a point. But the precision of alignment required for lightcoupling into and out of the fiber is not high. Also, stray lightfiltering can be accomplished with relatively angle loose tolerances. Sothis degree of accuracy is sufficient for a compact wide angle lens. Theconforming cup fiber bundle 555 can be included in a monocentric lensimage delivery system, as shown in the FIG. 9.

CMOS image sensors can be fabricated using lenslets over each pixel,e.g., to concentrate light. For example, the disclosed technology canemploy light filtering techniques including light-guided CMOS pixels,which can be modified to introduce absorption of stray light. FIG. 5Cshows exemplary diagrams 591, 592, and 593 depicting light filteringinto light guided CMOS pixels, modified to introduce absorption of straylight, e.g., showing front-side illuminated (FSI) vs. back-sideilluminated (BSI) focal planes. The diagram 591 shows a conventional FSIpixel. The diagram 592 shows a conventional FSI pixel with an exemplarylightguide designed to collect all the light incident on the pixellenslet surface. The diagram 593 shows an exemplary modified focal planepixel, which is configured to absorb large-angle (stray) light. Forexample, some manufacturers use an internal waveguide to increase lightcollection in each pixel. Typically, the goal is to transfer as muchlight as possible to the sensor. However, the same function can beprovided using the disclosed tapered fiber bundle using intentionallight stripping and filtering in the focal plane itself, e.g., either byshaping the light guide to intentionally strip large angle light orusing a lower index contrast waveguide, in combination with introducingan absorbing material between the light guides to absorb the light whichis not guided. In some implementations, for example, the focal plane canbe designed so that the undesired large angle light is absorbed, or itcan be designed so that the large angle light is reflected. In bothexemplary cases, the undesired large angle light is not detected, andthe use of the focal plane's restrictions on light transmission anglethen acts as a stray light filter, or virtual iris, in an imaging systemof the disclosed technology.

For example, if the fiber bundle is to be used to strip stray light, theangle of incidence of the light into the fiber should to be wellcontrolled. For example, if the focal plane is to be used to strip straylight, the angle of incidence into the focal plane should be wellcontrolled. For example, if the focal plane is to be used to strip straylight from the light after transmission through the fiber bundle, theangle of incidence into the fiber, as well as the angle of incidenceinto the focal plane, should be well controlled.

For these types of exemplary imagers, it can be advantageous to have theoptical fiber bundle shaped so the fiber cores are oriented radiallyfrom the center of the monocentric lens, and then curve to becomeperpendicular from the focal plane, as exemplified by the curved fiberbundle 555 shown in FIG. 5B.

In another aspect, a method for fabricating a monoconcentric opticalimaging system includes forming a flat slab of having fibers beingparallel to one another and perpendicular to the flat slab surfaces,bonding the flat slab onto a flat surface of a wafer to form a bondedstructure, processing an exposed surface of the flat slab bonded ontothe wafer to form spherical surface depressions at different locations,and engaging monocentric optical imaging modules to the sphericalsurface depressions, respectively, so that each spherical surfacedepression serves as a curved imaging surface for forming images by acorresponding monocentric optical imaging module.

Implementations of the method for fabricating a monoconcentric opticalimaging system can optionally include one or more of the followingexemplary features. In some implementations, for example, the method caninclude, before engaging the monocentric optical imaging modules to thespherical surface depressions, forming a textured surface layer over thespherical surface depressions for enhancing optical coupling into thefibers. In some implementations, for example, the method can includeseparating the bonded structure into individual modules where eachseparated module includes a spherical surface depression and amonocentric optical imaging module. For example, the separating step canbe performed before the engaging step. For example, the separating stepcan be performed after the engaging step. For example, the forming ofthe textured surface layer over the spherical surface depressions caninclude forming a layer of material over the spherical surfacedepressions, and patterning the layer of the material to form thetextured surface layer. For example, the patterning of the layer of thematerial can include an embossing process. For example, the forming ofthe textured surface layer over the spherical surface depressions caninclude directly patterning a top surface of each spherical surfacedepression to form a patterned top surface as the textured surfacelayer. For example, the forming of the textured surface layer over thespherical surface depressions can include a molding process. Forexample, the wafer can include imaging circuits at different locationsthat correspond to different the spherical surface depressions and thatare separated when separating the bonded structure into individualmodules, in which each imaging circuit includes optical detectors forreceiving light from the fibers. For example, each imaging circuit caninclude CCD or CMOS imaging sensing elements.

In another aspect, an optical imaging system includes a substrate, aflat slab bonded over the substrate, the flat slab having fibers beingparallel to one another and perpendicular to the flat slab surfaces andconfigured to include spherical surface depressions at differentlocations on top of the flat slab, and monocentric optical imagingmodules engaged to the spherical surface depressions, respectively, sothat each spherical surface depression serves as a curved imagingsurface for forming images by a corresponding monocentric opticalimaging module.

Implementations of the optical imaging system can optionally include oneor more of the following exemplary features. In some implementations,for example, the system can further include a textured surface layerformed on each spherical surface depression for enhancing opticalcoupling from a respective monocentric optical imaging module into thefibers via the spherical surface depression. In some implementations,for example, each optical fiber includes a tapered fiber core of a crosssection that varies along the optical fiber to select desired collectedlight rays to pass through the optical fiber while rejecting undesiredcollected light rays from being transmitted to an output facet of theoptical fiber.

FIGS. 6-8 show illustrative process diagrams of exemplary wafer-scalefabrication techniques to produce straight fiber bundles. In the examplein FIG. 6, the exemplary fabrication technique can include a process 811to form a slab of optical fibers (e.g., optical fiber cores surroundedby cladding) that are substantially parallel to one another andperpendicular to at least one flat surface. The exemplary fabricationtechnique can include a process 812 to attach the flat surface of theoptical fibers slab onto a flat surface of a wafer to form a bondedstructure. For example, the wafer can be configured as a silicon-basedCMOS wafer with multiple focal planes, and including electricalinterconnects configured in a ball and grid array. The exemplaryfabrication technique can include a process 813 to form one or morespherical surface depressions at different locations, e.g., that arealigned with focal planes. For example, the process 813 can includerotationally cutting or embossing the surface depressions into theexposed side of the optical fiber slab. The exemplary fabricationtechnique can include a process 814 to separate the bonded structureinto individual modules, in which each separated module includes one ormore spherical surface depressions and is diced to discretefiber-coupled focal planes.

In the example in FIG. 7, the exemplary fabrication technique caninclude a process 821 to form a slab of optical fibers (e.g., opticalfiber cores surrounded by cladding) that are substantially parallel toone another and perpendicular to at least one flat surface. Theexemplary fabrication technique can include a process 822 to attach theflat surface of the optical fibers slab onto a flat surface of a waferto form a bonded structure. For example, the wafer can be configured asa silicon-based CMOS wafer with multiple focal planes, and includingelectrical interconnects configured in a ball and grid array. Theexemplary fabrication technique can include a process 823 to form one ormore spherical surface depressions at different locations, e.g., thatare aligned with focal planes. For example, the process 823 can includerotationally cutting or embossing the surface depressions into theexposed side of the optical fiber slab. The exemplary fabricationtechnique can include a process 824 to form a textured surface layerover the one or more spherical surface depressions, e.g., which canenhance optical coupling into the fibers in each of the one or morespherical surface depressions. For example, the process 824 can includeforming a coating layer of material over the one or more sphericalsurface depressions, e.g., formed as a liquid coating and then molded tothe surface relief pattern, and subsequently patterning the coatinglayer to form the textured surface layer by applying an embossing toolto the coating layer. The exemplary fabrication technique can include aprocess 825 to separate the bonded structure into individual modules, inwhich each separated module includes at least one spherical surfacedepression with the surface relief pattern and is diced to discretefiber-coupled focal planes.

In the example in FIG. 8, the exemplary fabrication technique caninclude a process 831 to form a slab of optical fibers (e.g., opticalfiber cores surrounded by cladding) that are substantially parallel toone another and perpendicular to at least one flat surface. In theexample of FIG. 8, the slab of optical fibers are fabricated withspatially patterned features for light absorption, or with fiber coresstructured to facilitate coupling for specific angles of incidence. Theexemplary fabrication technique can include a process 832 to attach theflat surface of the optical fibers slab onto a flat surface of a waferto form a bonded structure. For example, the wafer can be configured asa silicon-based CMOS wafer with multiple focal planes, and includingelectrical interconnects configured in a ball and grid array. Theexemplary fabrication technique can include a process 833 to form one ormore spherical surface depressions at different locations, e.g., thatare aligned with focal planes. For example, the process 833 can includerotationally cutting or embossing the surface depressions into theexposed side of the optical fiber slab. The exemplary fabricationtechnique can include a process 834 to separate the bonded structureinto individual modules, in which each of the one or more separatedmodule includes a spherical surface depression and is diced to discretefiber-coupled focal planes.

Each of the exemplary fabrication techniques of FIGS. 6-8 can furtherinclude a process to engage a monocentric optical imaging module to aseparated module, produced of any of the described techniques, so thatthe spherical surface depression serves as a curved imaging surface forforming images by the monocentric optical imaging module.

FIG. 8B shows a diagram of an exemplary embossing tool to create andshape surface relief patterns for improved fiber coupling. For example,the exemplary embossing tool can be implemented (e.g., pressed down) toform a surface shape on a coating over spherical fiber bundle surface,as illustrated in the diagram of FIG. 8B.

FIG. 8C shows a diagram of an exemplary rotating cutting tool to createand shape surface relief patterns for improved optical fiber coupling.For example, the exemplary rotating cutting tool can be implemented tocut directly into fiber bundle material, e.g., to form an exemplarystepped surface pattern, as illustrated in the diagram of FIG. 8C.

FIG. 9 shows a diagram of an exemplary imaging system 900 including amonocentric lens with curved fiber bundle image delivery system andcolor CMOS array having pixels pitch two times less than fiber diameterat the output. The monocentric imaging system 900 is structured toinclude an optical fiber bundle 901 having concave surface configuredfrom a tapered bundle, e.g., such as the curved fiber bundle 555 shownin FIG. 5B. The optical fiber bundle 901 can be structured to includefiber cores are configured to be substantially normal to the light conesthat transfer light without enlarging the cone angle. While fibers canhave the low input NA to restrict stray light, in this exemplaryconfiguration, the fibers of the optical fiber bundle 901 can beconfigured with an NA=1, e.g., to collect all incident light into thefiber. Because the light incident on the face of the curved fiber istransmitted through the fiber and emitted with a similar angle at theoutput face, the undesired large angle light is emitted with a largeangle. This large angle light can then be filtered and not sensed by asuitably designed CMOS detector 902 which has been structure to detectlight incident within a limited range of angles. One way to accomplishthis limitation on the acceptance angle of the detector is to introducespecific structures within the individual detector pixel. A color filtercan increase apparent resolution; one fiber core 903 illuminates one RGBsuper pixel which has four physical pixels.

FIG. 10 shows diagrams of exemplary “fish-shaped” fiber bundles 1001 and1002 for light guiding and stray light filtering. In one example, thecurved fiber bundle 555 can be combined with an hourglass shaped fiber,e.g., like that of hourglass-shaped optical fiber bundle 503, to createan exemplary fish-shaped overall bundle 1001, in which the light iscoupled between the two bundles 555 and 503 (e.g., with some spreading,even if the bundles are incoherent and the cores are not matched inpitch or laterally aligned). In one example, the fish-shaped opticalfiber bundle 1001 is an exemplary configuration using one curved fiberbundle 555 optically coupled to one hourglass-shaped optical fiberbundle 503. In another example, the fish-shaped optical fiber bundle1002 is an exemplary configuration using a plurality of curved fiberbundle structures 555 structured to form a single curved fiber bundlestructure 1055 that is optically coupled to a plurality ofhourglass-shaped optical fiber bundle structures 503. For example, ifthe total angle range of light to be coupled into any single fiberbundle is not large (e.g., 30 degrees), then the overall structureprovides for a good approximation to radially disposed fibers at theimage surface, substantially uniform stray light stripping at the fiberwaist, and substantially parallel light emission to couple into thefocal plane. Also, for example, if the angle subtended by each bundle issufficiently small, the curved face can be polished directly into thehourglass bundle.

FIG. 11 shows a diagram of an exemplary straight optical fiber bundle1100 having an overall concave input face and including a plurality ofoptical fibers each having a fiber core that is sensitive to the inputangle of light emitted into the optical fiber and the shape of theoptical fiber. The diagram of FIG. 11 shows the ray output resultingfrom illuminating three exemplary optical fibers 1101, 1102, and 1103 atthe concave input face of the straight fiber bundle 1100, e.g., whichshows a large variation in output light divergence based on thecurvature of the input face and the angle of incidence upon that curvedface. The optical fiber 1101 receives input light at a relatively largeangle of incidence, e.g., compared to that of the optical fibers 1102and 1101, such that the light is outputted from the straight opticalfiber bundle at greatly diverging output angles. The optical fiber 1102receives input light at a smaller angle of incidence to that of theoptical fiber 1103 but at a larger angle of incidence to that of theoptical fiber 1101, such that the light is also outputted from thestraight optical fiber bundle at diverging output angles. The opticalfiber 1103 is configured as the central fiber on the concave input faceof the straight fiber bundle 1100 and receives input light at arelatively small angle of incidence to that of the other optical fibers,such that the light is also outputted from the straight optical fiberbundle at similar angles to those of the input light. For example, suchdifference in the output divergence over the field can result inexcessive CMOS pixels crosstalk toward the edge of the field.

FIG. 12 shows a diagram of an exemplary monocentric optical imagingsystem 1200 including a primary monocentric imaging lens module 1205coupled to straight optical fibers 1201, 1202, and 1203, depicting thecoupling efficiency of light between the lens module 1205 and thestraight optical fibers and the output divergence of the light out ofthe straight fiber 1201, 1202, and 1203. For example, showing threefibers located at the center field, and two off-axis field points. Asshown in FIG. 12, the exemplary 2 mm focus monocentric lens module 1205depicts ray-tracing of three field points through the straight fibers1201, 1202, and 1203, in which the straight fiber 1203 is located at thecenter of the field, the straight fiber 1201 is located at the upperfield point of 30°, and the straight fiber 1202 is located at the fieldpoint located at 30° in the vertical direction and 25.5° in horizondirection. The exemplary optical fibers 1201, 1202, and 1203 have NA=1.The exemplary optical fiber bundle can be cemented to an exemplary CMOSsensor, e.g., with Norland 61 cement, so that the fibers output areimbedded into the medium with refraction index 1.56. As shown in theFIG. 12, the divergence increases with field angles.

FIG. 13 shows a diagram depicting a more detailed partial view of theray-tracing through the exemplary straight fibers 1201 and 1202 of themonocentric optical imaging system 1200.

FIG. 14 shows a diagram depicting the output of an exemplary opticalfiber of the monocentric optical imaging system 1200 located at a cornerfield point. For example, the skew coupling angle can create a vortexlike output with low intensity at the low divergence angles.

For example, to simulate sensor crosstalk, an imaging sensor was mountedat a 2 μm distance from the bundle output. In this example, the bundlewas cemented to the sensor with NOA61 optical cement. The fiber bundlepitch was configured to be 2.5 μm and the CMOS sensor pitch wasconfigured to be 1.75 μm. For example, it was supposed that light willbe very fast absorbed, and created electrons will be collected byelectrode having 50% from pixel square size. The results of theexemplary simulation are shown in FIG. 15.

FIG. 15 shows a diagram depicting the detected focal plane signal, e.g.,showing the adjacent pixel crosstalk resulting from the same three fieldpoints. In FIG. 15, an image 1501 shows an array of output signals forthe center of the field, an image 1502 shows an array of output signalsfor the upper field point, and an image 1503 shows an array of outputsignals for the corner field point. The excessive crosstalk especiallyfor the exemplary vortex-like fiber output at the corner field point isshown to spread into a radius spot of at least four pixels.

For example, to improve coupling efficiency and reduce crosstalk, thedisclosed technology includes techniques, devices and systems that curvethe overall fiber to align with the incident light cone, as shown inFIG. 16. FIG. 16 shows a diagram depicting the uniform output divergenceof an exemplary curved and tapered fiber bundle 1600 that is operablewith an exemplary monocentric lens so the principal rays of the lenssubstantially align with the fiber axis at input. The diagram of FIG. 16shows the ray output resulting from illuminating three exemplary curvedand tapered optical fibers 1601, 1602, and 1603 at the concave inputface of the curved and tapered fiber bundle 1600, e.g., which shows nosubstantial variation in output light divergence based on the curvatureof the input face. For example, each of the curved optical fibers can beconfigured with a tapered optical fiber core surrounded by the exteriorcladding, e.g., similar to the hourglass-tapered fiber configurationshown in FIG. 4B. For example, the optical fiber 1601 receives inputlight at a relatively large angle of incidence, e.g., compared to thatof the optical fibers 1602 and 1601, but outputs the light atsubstantially the same angle as those of the optical fibers 1602 and1601.

Additionally, for example, the disclosed technology includes techniques,devices and systems that tilt the light cone to align with the fiber.One example includes using a thin conformal layer 1701, e.g., patternedwith micro optics along peripheral optical fibers of the concave inputface to deflect the input light at optical angles similar to that ofthose of optical fibers aligned along the center field, as shown in FIG.17. FIG. 17 shows a diagram depicting light coupling into and out of anexemplary straight fiber bundle 1700 with a concave input face, in whichthe concave surface has been modified with beam-deflecting features(e.g., holographic or lithographic input structure) to improveuniformity of output divergence.

FIG. 18 shows a diagram of a magnified view of the exemplary straightfiber bundle 1700 from the diagram of FIG. 17, e.g., showing thevariation in spatial features of exemplary structures 1801 for inputlight angle deflection. In some examples, the structures 1801 caninclude titled micro-prism facets conformed like Fresnel lenses.

FIG. 19 shows a diagram of an exemplary monocentric imaging system 1900including a wide-field monocentric lens operating in a “virtual” irismode and including substantially uniform transmission as a function ofillumination angle. The monocentric imaging system 1900 includes a“virtual” aperture stop provided by the exemplary hourglass taperedoptical waveguides. For example, the monocentric imaging system 1900 isfree from the image illumination reduction toward the edges of field ofview.

The monocentric optical imaging system 1900 can include a monocentricoptical imaging module 1901 including one or more optical elementshaving concentric surfaces to collect light and form an image on acurved image surface 1902. The monocentric optical imaging system 1900can include one or more optical waveguide bundles 1903 each comprising aplurality of optical waveguides that are optically coupled to themonocentric optical imaging module at different locations to receivedifferent portions of the collected light at the curved image surface,respectively, in which each optical waveguide is configured to have atapered waveguide core of a cross section that varies along the opticalwaveguide to select desired collected light rays to pass through theoptical waveguide while rejecting undesired collected light rays frombeing transmitted to an output facet of the optical waveguide. Forexample, each optical waveguide includes a waveguide section having across section in the tapered waveguide core to first decrease along adirection directed from the curved image surface to a correspondingimaging sensor and then to increase along the direction directed fromthe curved image surface to the corresponding imaging sensor. Themonocentric optical imaging system 1900 can include one or more imagingsensors 1904 configured on a planar surface and configured to receiveoutput light from the one or more optical waveguide bundles and todetect the received output light, the one or more imaging sensorsconfigured to produce a representation of the image on the curved imagesurface of the monocentric optical imaging module.

III. Focus of Monocentric Lenses

In another aspect, a method for optical imaging using a monocentricoptical imaging module includes operating a monocentric optical imagingmodule including one or more optical elements having concentric surfacesto collect light from a scene at a first object plane to be imaged andto form an image of the first object plane on a curved image surfacewhich is part of a spherical surface that is concentric with the one ormore optical elements having concentric surfaces, and, without adjustinga position or curvature of the curved image surface, adjusting an axialtranslation position of the monocentric optical imaging module to changefocusing of an object on the first object plane onto the curved imagingsurface to focusing of an object on a second object plane onto thecurved imaging surface, in which the second object plane is parallel tothe first object plane but is at a different axial location from thefirst object plane.

Implementations of the method for optical imaging using a monocentricoptical imaging module can optionally include one or more of thefollowing exemplary features. For example, in some implementations, themethod can further include using an array of optical waveguide bundleseach comprising a plurality of optical waveguides to optically couple tothe monocentric optical imaging module at different locations to receivedifferent portions of the collected light at the curved image surface,respectively, using an array of imaging sensors respectively coupled tothe array of the optical waveguide bundles to detect output light fromthe optical waveguides in each optical waveguide bundle to form apartial image of a full image in the collected light by the monocentricoptical imaging module in each imaging sensor, and combining partialimages of the imaging sensors to collectively form a representation ofthe full image on the curved image surface. For example, in someimplementations, the method can further include digitally reducing imageblurring caused by optical crosstalk of the guided light betweenadjacent optical waveguides. For example, in some implementations, themethod can further include using tapered optical waveguides coupledbetween the curved image surface and one or more imaging sensors todirect an image formed on the curved imaging surface to the one or moreimaging sensors so as to select desired light on the curved imagingsurface to reach the one or more imaging sensors while preventingundesired light on the curved imaging surface from reaching the one ormore imaging sensors. For example, in some implementations, the methodcan further include using optical waveguides coupled between the curvedimage surface and one or more imaging sensors to direct an image formedon the curved image surface to the one or more imaging sensors, andusing a textured surface structure over facets of the optical waveguidesfor receiving light from the curved imaging surface to enhance opticalcoupling from the curved imaging surface into the optical waveguides.

In another aspect, an optical imaging system includes a monocentricoptical imaging module including one or more optical elements havingconcentric surfaces and a curved imaging surface, the monocentricoptical imaging module configured to collect light to form an image onthe curved imaging surface, one or more imaging sensors each includingan array of optical detectors located away from the curved imagingsurface to receive light from the imaging surface and to convert thereceived light into detector signals, and an actuator coupled to the oneor more optical elements having concentric surfaces and configured toadjust an axial translation position of the one or more optical elementshaving concentric surfaces relative to the curved imaging surface, alongan optical axis from the one or more optical elements having concentricsurfaces to the curved imaging surface, to change focusing of an objectin a first object plane onto the same curved imaging surface to focusingof an object in a second, separate object plane onto the curved imagingsurface, in which the first and second object planes are at differentaxial locations from each other.

Implementations of the optical imaging system can optionally include oneor more of the following exemplary features. For example, the actuatorcan include a voice coil actuator. In some implementations, for example,the optical imaging system also can include a flexure support coupled tothe one or more optical elements having concentric surfaces. In someimplementations, for example, the optical imaging system also caninclude optical waveguides coupled between the curved imaging surface ofthe monocentric optical imaging module and the one or more imagingsensors to receive light from the curved imaging surface and configuredto deliver the received light to the one or more imaging sensors. Forexample, each of the optical waveguides can be configured to selectivelydeliver a desired portion of the received light to the one or moreimaging sensors while suppressing undesired stray light from reachingthe one or more imaging sensors so that each optical waveguideeffectuates an optical aperture stop with a limited angle range forreceiving light by the one or more imaging sensors. For example, each ofthe optical waveguides can be tapered in cross section. In someimplementations, for example, the optical imaging system also caninclude a textured surface structure over input facets of the opticalwaveguides to enhance optical coupling from the imaging surface into theoptical waveguides. For example, the textured surface structure can beoptically reflective. For example, the textured surface structure can beoptically refractive. For example, the textured surface structure can beoptically diffractive.

FIG. 20B shows a schematic diagram of an exemplary monocentricmicro-scale imager device 2000 capable of focusing using an axialtranslation motion. For example, the exemplary monocentric imager device2000 can be configured with an ultra-compact form factor. The imagerdevice 2000 includes a monocentric optical imaging module 2001 includingan interior optical elements 2001 a and an outer lens element 2001 bhaving concentric surfaces and a curved imaging surface 2002. Themonocentric optical imaging module 2001 is configured to collect lightto form an image on the curved imaging surface 2002. The imager device2000 can include imaging sensors 2005, e.g., each including an array ofoptical detectors located away from the curved imaging surface toreceive light from the imaging surface and to convert the received lightinto detector signals. The imager device 2000 can include opticalwaveguides 2004 optically coupled to and between the curved imagingsurface 2002 of the monocentric optical imaging module 2001 and theimaging sensors 2005 to receive light from the curved imaging surface2002 and deliver the received light to the imaging sensors 2005. Theimager device 2000 can include a voice coil actuator 2006 coupled to theoptical elements 2001 a and 2001 b to adjust an axial translationposition of the optical elements of the monocentric optical imagingmodule 2001 relative to the curved imaging surface 2002 to changefocusing of an object in a first object plane onto the curved imagingsurface to focusing of an object in a second, separate object plane ontothe curved imaging surface, in which the first and second object planesare at different axial locations from each other. The imager device 2000can include a flexure support arm 2007 coupled to the monocentricoptical imaging module 2001. The imager device 2000 can include anarmature / light block 2008 mechanically coupled to theactuator 2006 totranslate the monocentric optical imaging module 2001 relative to thecurved imaging surface 2002.

For example, photographic lenses are normally focused by moving themcloser or further from the image plane, but this appears impractical forthe deep spherical image surface in a wide-field monocentric lens. Foran exemplary 70 mm focal length objective, e.g., such as the objectiveof the monocentric primary lens 101 a of FIG. 1A, a 1 mm axialtranslation to focus on an object at 5 m range brings the image surfaceonly 0.5 mm closer to the objective for an object at a 60° field angle,and 0.17 mm closer for an object at an 80° field. This seems to implythat the lens can only focus in one direction at time, and needs 3dimensional translations to do so. In the monocentric multi-scaleimager, the primary lens position is fixed, and the secondary imagersare used for independent focus on each region of the scene. However,introducing optomechanical focus mechanism for each secondary imagerconstrains the lens design, and adds significantly to the overall systembulk and cost. More fundamentally, the exemplary monocentric-waveguideimager 102 shown in FIG. 1B has no secondary imagers, and cannot befocused in this way, which initially appears a major disadvantage. Infact, however, axial translation of monocentric lenses maintains focuson a planar object across the full field of view.

Consider the geometry of an image formation in the monocentric lensstructure shown in FIG. 20A. For a focal length f with refocusing fromobject at infinity to the closer on-axis object at distance d, assumingd>>f, the image surface shift Δx is:

$\begin{matrix}{{\Delta\; x} = {\frac{f^{2}}{d - f} \approx \frac{f^{2}}{d}}} & (1)\end{matrix}$For the off-axis field point B, having a field angle and the angle ofprincipal ray β₁, the distance OB to the object is d/cos (β₁) and therefocusing image point shift Δx′ (B_(inf)B′) Will be

$\begin{matrix}{{\Delta\;{x^{\prime}\left( \beta_{1} \right)}} = {{f^{2}\frac{\cos\left( \beta_{1} \right)}{d}} = {\left. {\Delta\; x\;{\cos\left( \beta_{1} \right)}}\Rightarrow\overset{\_}{B_{\inf}Q} \right. = {\frac{\Delta\;{x^{\prime}\left( \beta_{1} \right)}}{\cos\left( \beta_{1} \right)} = {{\Delta\; x} = \overset{\_}{A_{\inf}^{\prime}A^{\prime}}}}}}} & (2)\end{matrix}$which means that for refocusing, the spherical image surface 5(∞) isaxially translated on segment Δx to the position 5(d). As will be shownlater, for the exemplary 12 mm focus monocentric lens this approximationworks well for up to the closest distance of 500 mm, and reasonably wellfor objects at a 100 mm range. So for a planar object at any distanceabove some moderate minimum, the geometry of refocusing the monocentriclens is in accordance with first order paraxial optics.

The most general analytic tool for lens aberration analysis andcorrection is classical 3^(rd) order Seidel theory. In Seidel theoryastigmatism and image curvature are bound with the coefficients C and D.Referring to the variables defined in FIG. 21, the coefficients C and Dare shown in Eq. (3) and (4) can be expressed as:

$\begin{matrix}{C = {\frac{1}{2}{\sum\limits_{s = 1}^{m}{{h_{s}\left( \frac{\beta_{s + 1} - \beta_{s}}{\frac{1}{n_{s + 1}} - \frac{1}{n_{s}}} \right)}^{2}\left( {\frac{\alpha_{s + 1}}{n_{s + 1}} - \frac{\alpha_{s}}{n_{s}}} \right)}}}} & (3) \\{D = {{\frac{1}{2}{\sum\limits_{s = 1}^{m}\frac{\left( {\frac{1}{n_{s}} - \frac{1}{n_{s + 1}}} \right)}{r_{s}}}} + C}} & (4)\end{matrix}$where r_(i) is radius of i^(th) surface and n_(i) is the preceding indexof refraction. From the diagram of FIG. 20A, it is clear that chief rayangles to optical axis at each surface are identical (β₁=β₂=β₃=β₄) forany axial position of the monocentric optics relative to image surface.Therefore, coefficient C remains zero while focusing to planar objectsurfaces by means of axial movement of the monocentric objective lens. Cand D can be expressed as:

$\begin{matrix}{C = {{\frac{1}{4n_{im}}\left( {\frac{1}{R_{t}} - \frac{1}{R_{s}}} \right)\mspace{14mu}{and}\mspace{14mu} D} = {\frac{1}{2n_{im}}\frac{1}{R_{s}}}}} & (5)\end{matrix}$where R_(t) is the tangential image surface radius, R_(s) is thesagittal image surface radius, and n_(im) is the image space refractionindex. So if C is defined as zero during refocusing then R_(t) will beequal to R_(s) and the image surface will stay spherical and maintainthe image radius R_(im)=R_(t)=R_(s). Also, from Eq. (4) it is clear thatthe coefficient D will remain constant. Because D remains constantequations (5) also show that R_(s) and hence radius R_(im) will stayunchanged as well. Third order aberration theory couples the imagecurvature with astigmatism, while coma and spherical aberrations need tobe corrected at this surface. In other words, third order Seidelaberration theory also indicates that simple axial refocusing ofmonocentric lens structures preserves the image surface radius,maintaining focus for a planar object onto a spherical image surfaceover a wide range of object distances. In a purely monocentric geometrythere is zero coma, and no additional coma will be introduced bytranslation. Suppose that spherical aberration is corrected at infinity.Third order spherical aberration does not have the term, which dependson the object distance. For example, only a minor change in sphericalaberration during refocusing is expected, e.g., due to the small changesin terms (α_(i+1)−α_(i))², which constitutes the Seidel sphericalaberration coefficient. This is confirmed by the ZEMAX simulations shownin Section IV for an optimal f=12 mm lens solution.

IV. Systematic Design of the Two Glass Monocentric Lens

In another aspect, an optical imaging system includes a monocentricoptical imaging module having concentric optical surfaces that collectlight in a photographic visible spectrum to form an image on a curvedimaging surface that is concentric with the concentric optical surfacesof the monocentric optical imaging module, in which the monocentricoptical imaging module includes an inner glass ball lens of a spherehaving a low index and an outer glass lens element of a high indexglass, one or more imaging sensors each including an array of opticaldetectors located away from the imaging surface to receive lightrepresenting the image initially formed on the curved imaging surfaceand to convert the received light into detector signals, and opticalwaveguides coupled between the imaging surface and the one or moreimaging sensors to receive light from the curved imaging surface anddeliver the received light to the one or more imaging sensors.

Implementations of the optical imaging system can optionally include oneor more of the following exemplary features. For example, the outerglass lens element of the high index glass can include a glass materialof S-LAH79, N-LASF46A, TAFD40, K-GIR79, S-LAH79, K-PSFN2, K-PSFN203, orP-SF68, and the inner glass ball lens of the low index can include aglass material of K-LASFN9, TAF5, S-LAH59, M-TAF1, MC-TAF1, TAF5,S-LAH59, K-LAFK50, M-TAFD305, LAF2, S-LAM2, M-TAF1, K-LaFK50T, S-LAL59,K-LaKn12, TAC4, TAF4, N-LAF21, TAF1, S-LAH64, K-VC80, S-LAL13, M-LAC130,P-LAK35, LAC13, N-LASF45, N-LASF45HT, S-LAM66, BAFD8, or S-BAH28. Forexample, the outer glass lens element of the high index glass and theinner glass ball lens of the low index can be configured to minimize athird order spherical aberration while minimizing monochromatic andchromatic aberrations.

In another aspect, a method for designing a monocentric optical imagingmodule having concentric optical surfaces that collect light to form animage on a curved imaging surface that is concentric with the concentricoptical surfaces of the monocentric optical imaging module, in which themonocentric optical imaging module includes an inner glass ball lens ofa sphere having a low index and an outer glass lens element of a highindex glass, in which the method includes: determining surface radii ofthe inner glass ball and outer glass lens element to minimize 3rd orderSeidel spherical and axial chromatic aberrations for combinations ofglass materials for the inner glass ball and outer glass lens element;optimizing lens prescriptions of the inner glass ball and outer glasslens element via ray tracing of multiple ray heights for a centralwavelength within the photographic visible spectrum to generate lensdesign candidates based on the combinations of glass materials for theinner glass ball and outer glass lens element; computing a polychromaticmean RMS wavefront deformation to generate a ranked list of lens designcandidates for the combinations of glass materials for the inner glassball and outer glass lens element; and confirming the ranked order bycomparing polychromatic diffraction modulation transfer function (MTF)curves of the lens design candidates.

Despite the structural constraints, even a simple two-glass monocentricobjective lens can provide high angular resolution over the sphericalimage surface. With waveguide image transfer, an overall systemresolution is directly limited by objective lens resolution. Inmulti-scale imagers, geometric aberrations in the objective can becorrected by configuring objective-specific relay optics. However,compensating for large aberrations in the primary lens tends to increasethe complexity and the precision of fabrication of the relay optics. Forexample, since each multi-scale imager requires many sets of relayoptics (e.g., such as 221 sets in the 120° field 2.4 Gigapixel imagerdesign), minimizing relay optic complexity and fabrication tolerance cansignificantly reduce system cost. So for both structures, it is usefulto optimize the objective lens resolution.

As previously shown in FIG. 1B, the exemplary Gigapixel monocentricmulti-scale imager 102 integrates a mosaic of sub-images via fiberbundle waveguides 106. In some embodiments, for example, the fiberbundles 106 can be configured as curved and/or tapered waveguide fiberbundles 1001 according to the optical layout diagram shown in FIG. 10.

Optical systems are now typically designed by computer numericoptimization in software, e.g., which can include using commercialsoftware like Zemax and CodeV. The highly constrained monocentric lensesseem well suited to a global optimization search to identify the bestglass combination and radii. However, for example, “blind” optimizationof monocentric lenses, even a simple two-glass lens, often overlooks thebest solutions. This can be especially true for large NA designs, wherethe ray angles are steep and the optimization space has multiple deeplocal minima There are also a large number of glasses to consider. Forexample, a currently available glass catalog was recently increased by anumber of new glasses including 559 glasses. The more advancedoptimization algorithms take significant processing time. Even for a twoglass lens it is impractical to use them to search all 312k potentialcombinations, so the best design may be overlooked. Fortunately, thesymmetry of monocentric lenses permits a relatively straightforwardmathematical analysis of geometrical optic aberrations, as well asproviding some degree of intuitive understanding of this overall designspace. Combining previous analysis techniques with computer sorting ofglass candidates can enable a global optimization for any specific focallength and spectral bandwidth desired.

In this section, a detailed analysis is provided for the design oftwo-glass monocentric lenses. The detailed analysis begins with thefirst order paraxial and Seidel third order analysis of the focus ofwide-field monocentric imagers, showing that despite the highly curvedfocal surface, axial translation of monocentric lenses can maintainfocus of a planar object field from infinite to close conjugates. Later,the systematic optimization of these lenses is demonstrated by thefollowing these exemplary process.

The exemplary process includes, for a specified focal length, numericalaperture, and wavelength range:

-   (1) compute and minimize 3rd order Seidel spherical and axial    chromatism aberrations to find approximate surface radii for valid    glass combination;-   (2) optimize lens prescriptions via exact ray tracing of multiple    ray heights for the central wavelength;-   (3) calculate the polychromatic mean RMS wavefront deformation, and    generate ranked list of all lens candidates; and-   (4) confirm ranking order by comparing polychromatic diffraction    modulation transfer function (MTF) curves.

To verify this exemplary method, the objective from the exemplary 2.4Gigapixel multi-scale imager was redesigned, in which the globaloptimization process yields the original exemplary design (andfabricated) lens, as well as additional candidates with improvedinternal image surface resolution. An exemplary design methodology wasapplied to a new system, e.g., an ultra-compact fiber-coupled imagerwith a 12 mm focal length and uniform resolution and light collectionover more than 120° field of view. This exemplary design comparesfavorably to a more conventional imager using a “fisheye” wide fieldlens in exemplary implementations performed and described herein.

Imaging optics are conventionally designed in two steps. First,monochromatic design at the center wavelength achieves a sufficientlevel of aberrations correction. The second step is to correct chromaticaberration, usually by splitting some key components to achieveachromatic power: a single glass material is replaced with two glassesof the same refraction index at the center wavelength, but differentdispersions. However, this process cannot easily be applied to theexemplary symmetric two glass monocentric lens shown in FIG. 21. For agiven glass pair and focal length, lens has only four prescriptionparameters to be optimized (two glasses and two radii), and the radiiare constrained with the monocentric symmetry and desired focal length.In place of this lens design procedure, a systematic search process isdefined beginning with a specified focal length, F/number, andwavelength range.

Optimization of each glass combination was done in three steps. Thefirst step is to determine the solution (if it exists) to minimize thirdorder Seidel geometrical and chromatic aberrations. A monocentric lensoperating in the “fiber” stop mode has only two primary third orderaberrations—spherical aberration (Seidel wave coefficient W₀₄₀) andchromatism of position W₀₂₀, which is defocus between blue and redparaxial foci. The sum of the absolute values of the third ordercoefficients provide a good approach for a first-pass merit (cost)function, and an analytical solution for third order coefficients allowsthis cost function to be quickly calculated.

FIG. 21 shows a diagram depicting third order aberration theory appliedto monocentric lens design. The exemplary monocentric lens shown in FIG.21 is defined with 6 variables, the two radii r₁ and r₂, and the indexand Abbe number for each of two glasses: the outer glass n₂ and v₂, andthe inner glass n₃ and v₃. Ray-tracing of any collimated ray can use theAbbe invariant:

$\begin{matrix}{{r_{i} = {h_{i}\frac{n_{i + 1} - n_{i}}{{n_{i + 1}\alpha_{i + 1}} - {n_{i}\alpha_{i}}}}}{or}} & (6) \\{\alpha_{i + 1} = {{\frac{n_{i}}{n_{i + 1}}\alpha_{i}} + {h_{i}\frac{n_{i + 1} - n_{i}}{n_{i + 1}r_{i}}}}} & (7)\end{matrix}$where α_(i) are the angles between marginal rays and the optical axis.The ray-tracing proceeds surface by surface and at each step for theinput ray angle α_(i) and ray height h_(i) the output angle α_(i+1) canbe calculated by Eq. (7). The ray height at the next surface ish _(i+1) =h _(i)−α_(i+1) d _(i)  (8)where d_(i) is the thickness between surfaces i+1 and i. For themonocentric lens d₁=r₁−r₂, d₂=2r₂ and d₃=r₁−r₂. The ray trace of themarginal input ray having α₁=0 gives

$\begin{matrix}{\frac{1}{f} = {{\frac{2}{r_{1}}\left( {1 - \frac{1}{n_{2}}} \right)} + {\frac{2}{r_{2}}\left( {\frac{1}{n_{2}} - \frac{1}{n_{3}}} \right)}}} & (9)\end{matrix}$

For a given glass combination and focal length f Eq. (9) constrains theradius r₂ to the radius r₁ for all subsequent calculations.

The Seidel spherical aberration coefficient B can be expressed as:

$\begin{matrix}{B = {\frac{1}{2}{\sum\limits_{s = 1}^{4}{{h_{s}\left( \frac{\alpha_{s + 1} - \alpha_{s}}{\frac{1}{n_{s + 1}} - \frac{1}{n_{s}}} \right)}^{2}\left( {\frac{\alpha_{s + 1}}{n_{s + 1}} - \frac{\alpha_{s}}{n_{s}}} \right)}}}} & (10)\end{matrix}$Equivalently, the spherical wave aberration W₀₄₀ for the marginal rayis:

$\begin{matrix}{W_{040} = {{\frac{1}{4}B\;\rho^{4}}\overset{\rho = 1}{=}{\frac{1}{8}{\sum\limits_{s = 1}^{4}{{h_{s}\left( \frac{\alpha_{s + 1} - \alpha_{s}}{\frac{1}{n_{s + 1}} - \frac{1}{n_{s}}} \right)}^{2}\left( {\frac{\alpha_{s + 1}}{n_{s + 1}} - \frac{\alpha_{s}}{n_{s}}} \right)}}}}} & (11)\end{matrix}$where a clockwise positive angle convention is used.

The starting position for ray-tracing is h₁=f×NA and α₁=0. Consequently,applying the Abbe invariant for each surface can allow substituting rayangles and heights with the system constructional parameters. Thus, fromAbbe invariant for 1^(st) surface, one gets:

$\begin{matrix}{r_{1} = {{h_{1}\frac{n_{2} - 1}{n_{2}\alpha_{2}}\mspace{14mu}{or}\mspace{14mu}\alpha_{2}} = {h_{1}\frac{n_{2} - 1}{n_{2}r_{1}}}}} & (12)\end{matrix}$So α₂ can be determined from the input ray height and prescriptionparameters of the first surface. The value of h₂ is found from angle α₂(see Eq. (8)), and so on. Using this iterative process, and the relationbetween r₁ and r₂ from Eq. (9), one gets:

$\begin{matrix}{W_{040} = {h_{1}^{4}\begin{pmatrix}{{- \frac{\left( {n_{2}^{2} - {3n_{2}n_{3}} + n_{3}^{2}} \right)}{32{f^{3}\left( {n_{2} - n_{3}} \right)}^{2}}} - \frac{\left( {n_{2} - 1} \right)\left( {n_{2}^{2} - n_{3}} \right)\left( {n_{3} - 1} \right)}{4{n_{2}^{2}\left( {n_{2} - n_{3}} \right)}^{2}r_{1}^{3}} +} \\{\frac{\left( {n_{2} - 1} \right)^{2}\left( {n_{2}^{2} + {n_{2}n_{3}} + n_{3}^{2}} \right)}{8{{fn}_{2}^{2}\left( {n_{2} - n_{3}} \right)}^{2}r_{1}^{2}} - \frac{\left( {n_{2} - 1} \right)\left( {n_{2}^{2} + {n_{2}n_{3}} + n_{3}^{2}} \right)}{16f^{2}{n_{2}\left( {n_{2} - n_{3}} \right)}^{2}r_{1}}}\end{pmatrix}}} & (13)\end{matrix}$The defocus coefficient W₀₂₀ between images in blue and red light isequal to −L₀/2, where

$\begin{matrix}{L_{0} = {{{- 2}W_{020}} = {h_{1}^{2}\left( {\frac{\left( {n_{3} - 1} \right)\left( {{2{f\left( {1 - n_{2}} \right)}} + {n_{2}r_{1}}} \right)}{{f\left( {n_{2} - n_{3}} \right)}r_{1}n_{3}v_{3}} - \frac{\left( {n_{2} - 1} \right)\left( {{2{f\left( {1 - n_{3}} \right)}} + {n_{3}r_{1}}} \right)}{{f\left( {n_{2} - n_{3}} \right)}r_{1}n_{2}v_{2}}} \right)}}} & (14)\end{matrix}$Eq. (14) is sufficiently accurate for the visible (photographic)spectral range, where the dispersion is approximately linear. Design forextended visible waveband (400-700 nm) requires calculations in twoseparate sub-bands with custom defined Abbe numbers to compensate forthe increased nonlinearity of the glass dispersion curve.E(r₁)=|W₀₄₀|+|W₀₂₀| can be defined as a merit function for 3rd orderaberrations, which is continuous-valued and has a single global minimumidentifying the approximate (near optimum) radius r₁ for each valid twoglass combination. Afterwards, radius r₂ is calculated from Eq. (9).

The result is an algebraic expression for the 3rd order aberrations ofthe solution—if any—for a given glass combination. In the examples, thiscalculation was performed for each of the 198,000 combinations of the446 glasses, e.g., which were available in the combined Schott, Ohara,Hikari and Hoya glass catalogs, which are incorporated by reference aspart of the disclosure of this patent document. This yields a list ofqualified candidates (those forming an image on or outside of the outerglass element), ranked by third order aberrations. However, this rankingis insufficiently accurate for a fully optimized lens.

Because of high numerical aperture, monocentric systems tend to havestrong 5^(th) and 7^(th) order aberrations. That makes 3^(rd) orderanalysis only a first approximation towards a good design. Fortunately,the two-glass monocentric lens system has an exact analytical ray tracesolution in compact form, and the more accurate values of the lensprescription parameters can be found from a fast exact ray-tracing ofseveral ray heights.

The variables for ray-tracing of rays with arbitrary input height h isshown in FIG. 22, where φ_(i) are the angles between the ray and thesurface normal. One can write

$\begin{matrix}{{\sin\left( \phi_{1} \right)} = \frac{h}{r_{1}}} & (15)\end{matrix}$From Snell's law, one has:

$\begin{matrix}{{\sin\left( \phi_{1}^{\prime} \right)} = \frac{h}{r_{1}n_{2}}} & (16)\end{matrix}$Applying the sine law for the triangle ABO yields

$\begin{matrix}{{\sin\left( \phi_{2} \right)} = {{\frac{r_{1}}{r_{2}}{\sin\left( \phi_{1}^{\prime} \right)}} = {{\frac{r_{1}}{r_{2}}\frac{h}{r_{1}n_{2}}} = \frac{h}{r_{2}n_{2}}}}} & (17)\end{matrix}$Again from Snell's law

$\begin{matrix}{{\sin\left( \phi_{2}^{\prime} \right)} = {{\frac{n_{2}}{n_{3}}{\sin\left( \phi_{2} \right)}} = {{\frac{n_{2}}{n_{3}}\frac{h}{r_{2}n_{2}}} = \frac{h}{r_{2}n_{3}}}}} & (18)\end{matrix}$Triangle OBC has equal sides OB and OC. So,

$\begin{matrix}{{\sin\left( \phi_{3}^{\prime} \right)} = {{\frac{n_{3}}{n_{2}}{\sin\left( \phi_{3} \right)}} = {{\frac{n_{3}}{n_{2}}\frac{h}{r_{2}n_{3}}} = \frac{h}{r_{2}n_{2}}}}} & (19)\end{matrix}$From triangle OCD, one can find

$\begin{matrix}{{\sin\left( \phi_{4} \right)} = {{\frac{r_{2}}{r_{1}}{\sin\left( \phi_{3}^{\prime} \right)}} = \frac{h}{r_{1}n_{2}}}} & (20)\end{matrix}$Then finally

$\begin{matrix}{{\sin\left( \phi_{4}^{\prime} \right)} = {{n_{2}{\sin\left( \phi_{4} \right)}} = \frac{h}{r_{1}}}} & (21)\end{matrix}$One exemplary result is that for the monocentric lens there is aninvariant in the form:φ₄′≡φ₁  (22)

Next, the segment OE=S can be found by applying the sine theorem to thetriangle OED:

$\begin{matrix}{{S = \frac{r_{1}{\sin\left( \phi_{4}^{\prime} \right)}}{\sin\left\lbrack {{180{^\circ}} - \left( {{180{^\circ}} - \phi_{4}^{\prime}} \right) - \left( {{180{^\circ}} - \phi_{1} - \phi_{22} - \phi_{33} - \phi_{44}} \right)} \right\rbrack}}\mspace{79mu}{or}} & (23) \\{\mspace{79mu}{S = \frac{r_{1}{\sin\left( \phi_{4}^{\prime} \right)}}{\sin\left( {{{- 180}{^\circ}} + {2\phi_{1}} + \phi_{22} + \phi_{33} + \phi_{44}} \right)}}} & (24)\end{matrix}$From Eq. (15)

$\begin{matrix}{\phi_{1} = {{arc}\;{\sin\left( \frac{h}{r_{1}} \right)}}} & (25)\end{matrix}$

From the triangles OAB, OBC and OCD, one has

$\begin{matrix}{\phi_{22} = {{\phi_{2} - \phi_{1}^{\prime}} = {{\arcsin\left( \frac{h}{r_{2}n_{2}} \right)} - {{arc}\;{\sin\left( \frac{h}{r_{1}n_{2}} \right)}}}}} & (26) \\{\phi_{33} = {{{180{^\circ}} - {2\phi_{2}^{\prime}}} = {{180{^\circ}} - {2\mspace{11mu}{\arcsin\left( \frac{h}{r_{2}n_{3}} \right)}}}}} & (27) \\{\phi_{44} = {{\phi_{3}^{\prime} - \phi_{4}} = {{{arc}\;{\sin\left( \frac{h}{r_{2}n_{2}} \right)}} - {{arc}\;{\sin\left( \frac{h}{r_{1}n_{2}} \right)}}}}} & (28)\end{matrix}$

Finally,

                                           (29)$S = \mspace{745mu}\mspace{76mu}{\quad\frac{h}{\sin\left\{ {2\left\lbrack {{\arcsin\left( \frac{h}{r_{1}} \right)} - {\arcsin\left( \frac{h}{r_{1}n_{2}} \right)} + {\arcsin\left( \frac{h}{r_{2}n_{2}} \right)} - {\arcsin\left( \frac{h}{r_{2}n_{3}} \right)}} \right\rbrack} \right\}}}$From Eq. (29) the longitudinal aberration for the ray with input heighth_(i) is given byΔS(h _(i))=S(h _(i))−f  (30)Radius r₂ is bound to radius r₁ with Eq. (9). With a given focal lengthand combination of refractive indices, the longitudinal aberration ΔS isactually a function of a single variable r₁. Finally, for the moreaccurate monochromatic optimization of the radius r₁, a more accuratecost function Q is obtained:

$\begin{matrix}{Q = {{\sum\limits_{i = 1}^{3}{{Abs}\left( {\Delta\;{S\left( {h_{i},\lambda} \right)}} \right)}} + {\sum\limits_{j = 1}^{3}{\sum\limits_{k \neq j}^{\;}{{Abs}\left\lbrack {{\Delta\;{S\left( {h_{j},\lambda} \right)}} - {\Delta\;{S\left( {h_{k},\lambda} \right)}}} \right\rbrack}}}}} & (31)\end{matrix}$

Where for visible light operation, λ is the n_(d) line located in centerof photographic waveband and three input ray heights are: h₁=f×NA,h₂=0.7h₁ and h₃=0.41h₁, respectively.

With such steep ray angles Q is a strongly varying function, which iswhy a fast automated optimization can overlook the optimal radius valuesfor a given glass pair. FIG. 23 shows an exemplary plot showingdependence of criterion Q on the radius r₁. FIG. 23 shows the dependenceof the Q on radius r₁ for a representative case, one of the best glasspairs (S-LAH79 and S-LAH59) for the 12 mm focal length lens described inlater in this section. The monochromatic image quality criterion Q hasseveral minimums over the possible range for r₁ radius. The preliminarysolution for r₁ radius for this glass pair obtained from the third orderaberrations minimization was 8.92 mm, close to the global minimumsolution for Q found at 9.05 mm. This shows how the first optimizationstep provided a good starting point for r₁ radius, avoiding the timeconsuming investigation of low quality solutions in the multi-extremumproblem illustrated by FIG. 23.

In the third step, the wavefront deformation is calculated and expandedinto Zernike polynomials. The polychromatic mean square root wavefrontdeformation (RMS) is calculated and used as a criterion for creating theranked list of monocentric lens solutions by means of their quality. Inthe monocentric lens geometry the aperture stop is located at the centerof the lens, where entrance and exit pupils coincide as well. This isshown in FIG. 24, which shows a diagram depicting image formation in anexemplary monocentric lens.

For an arbitrary ray the lateral aberrations ΔY are bound to thewavefront deformation as:

$\begin{matrix}{{\Delta\; Y} = {{- \frac{\partial W}{\partial\rho}}\frac{\lambda}{A}}} & (32)\end{matrix}$where W is the wavefront deformation expressed in wavelengths; ρ isreduced ray pupil coordinate which varies from zero at the pupil centerto unity at the edge; defining A as the back numerical aperture, and ΔYas the lateral aberration in mm From FIG. 24 one has

$\begin{matrix}{{\Delta\;{S(\rho)}} = {\frac{\Delta\; Y}{A\;\rho} = {{- \frac{\partial W}{\partial\rho}}\frac{\lambda}{A^{2}\rho}}}} & (33)\end{matrix}$where Aρ is coordinate of the ray in the image space. Expansion of thewavefront deformation into Zernike polynomials up to 7^(th) order isgiven by:

$\begin{matrix}{{{- \Delta}\;{S\left( {\rho,\lambda_{i}} \right)}\frac{A^{2}}{\lambda_{i}}} = {{4C_{20}} + {C_{40}\left( {{24\rho^{2}} - 12} \right)} + {C_{60}\left( {{120\rho^{4}} - {120\rho^{2}} + 24} \right)} + {C_{80}\left( {{560\rho^{6}} - {840\rho^{4}} + {360\rho^{2}} - 40} \right)}}} & (34)\end{matrix}$

The values for ΔS(ρ,λ_(i)) are calculated with fast ray-tracing (Eq.(30)) for nine rays with reduced coordinate heights ρ_(j)=1, 0.95, 0.9,0.85, 0.8, 0.75, 0.7, 0.6, 0.5 and for three wavelengths 470 nm, 550 nmand 650 nm. Then coefficients C_(n0)(λ_(i)) are calculated from theleast square criterion:

$\begin{matrix}{{\sum\limits_{j = 1}^{9}\begin{bmatrix}{{{- \Delta}\;{S\left( {\rho,\lambda_{i}} \right)}\frac{A^{2}}{\lambda_{i}}} - {4{C_{20}\left( \lambda_{i} \right)}} - {{C_{40}\left( \lambda_{i} \right)}\left( {{24\rho^{2}} - 12} \right)} -} \\{{{C_{60}\left( \lambda_{i} \right)}\left( {{120\rho^{4}} - {120\rho^{2}} + 24} \right)} -} \\{{C_{80}\left( \lambda_{i} \right)}\left( {{560\rho^{6}} - {840\rho^{4}} + {360\rho^{2}} - 40} \right)}\end{bmatrix}^{2}} = \min} & (35)\end{matrix}$

In order to prevent general defocus of the image surface due becausebounded was the radius r₂ and focus with third order equation (9),introduced was a small shift dS of the back focal distance which makesthe new coefficient C₂₀ ^(new)(λ₂=550 nm) equal to zero

$\begin{matrix}{{dS} = {4{C_{20}\left( \lambda_{2} \right)}\frac{\lambda_{2}}{A^{2}}}} & (36)\end{matrix}$This means that the system will have a slightly adjusted focusf^(new)=f+dS, and the only difference from before will be incoefficients C₂₀ ^(new):

$\begin{matrix}{{C_{20}^{new}\left( \lambda_{i} \right)} = {{C_{20}\left( \lambda_{i} \right)} - {{dS}\frac{A^{2}}{4\lambda_{i}}}}} & (37)\end{matrix}$

Finally, the system RMS wavefront deformation is:

$\begin{matrix}{{RMS} = {\frac{1}{3}{\sum\limits_{i = 1}^{3}\;\left\{ {\frac{\left\lbrack {C_{20}^{New}\left( \lambda_{i} \right)} \right\rbrack^{2}}{3} + \frac{\left\lbrack {C_{40}\left( \lambda_{i} \right)} \right\rbrack^{2}}{5} + \frac{\left\lbrack {C_{60}\left( \lambda_{i} \right)} \right\rbrack^{2}}{7} + \frac{\left\lbrack {C_{80}\left( \lambda_{i} \right)} \right\rbrack^{2}}{9}} \right\}}}} & (38)\end{matrix}$

In the examples, the top 50 solutions for different glasses combinationswere sorted in the ranked list by RMS quality performance, then each wasimported into ZEMAX optical design software and quickly optimized forthe best modulation transfer function (MTF) performance at the 200lp/mm. For example, this frequency was chosen because the smallest fiberbundle receiver 24AS, e.g., available from Schott, has 2.5 micronspitch. This close to the optimal design, however, the MTF performance iswell behaved, and a similar result is found with a wide range of MTFvalues.

V. Exemplary Two Glass Monocentric Cases

V.1 AWARE2 Monocentric Lens Analysis

The goal of this analysis is a monocentric lens optimization process tofind the best possible candidates for fabrication. These candidates arethen subject to other materials constraints involved in the finalselection of a lens design, including mechanical aspects such asdifferential thermal expansion or environmental robustness, as well aspractical aspects like availability and cost. The process describedabove appears to provide a comprehensive list of candidate designs.However, the best test of a lens design process is to compare theresults to one generated by the normal process of software based lensdesign. To do this, used was the constraints of a monocentric objective,for example, which was designed in the DARPA AWARE program;specifically, for example, the AWARE-2 objective lens, e.g., which wasdesigned by a conventional software optimization process, thenfabricated, tested, and integrated into the AWARE2 imager. The lens hasa 70 mm focal length and image space F# of 3.5, using a fused silicacore and a S-NBH8 glass outer shell. The optical prescription is shownin Table 1, and the layout of the embodiment 2801 in FIG. 25A.

TABLE 1 Optical prescription of the fabricated AWARE2 lens. Semi-Surface Type Radius Thickness Glass Diameter OBJ Standard InfinityInfinity 1 Standard 31.80000 13.61300 S-NBH8 29.69700 2 Standard18.18700 18.18700 F_SILICA 17.39400 STO Standard Infinity 18.18700F_SILICA 16.95200 4 Standard −18.18700 15.19100 S-NBH8 16.95200 5Standard −33.37800 36.87800 30.13600 IMA Standard −70.25600 60.84437

The global optimization method identified this candidate lens system, aswell as multiple alternative designs (glass combinations) which providea similar physical volume and improved MTF. The optical prescription ofthe top-ranked solution is shown in the Table 2, and the lens layout isshown as embodiment 2802 in FIG. 25B.

TABLE 2 Optical prescription of the top design solution for the AWARE2lens. Semi- Surface Type Radius Thickness Glass Diameter OBJ StandardInfinity Infinity 1 Standard 34.91298 17.95482 N-KZFS2 34.91298 2Standard 16.95816 16.95816 S-FPL53 16.95816 STO Standard Infinity16.95816 S-FPL53 7.00075 4 Standard −16.95816 17.95482 N-KZFS2 16.958165 Standard −34.91298 35.30018 34.91298 IMA Standard −70.21316 70.00000

The new candidate appears physically very similar to the fabricatedlens. However, the MTF 2901 and ray aberrations 2902 for manufacturedprototype and the top design solution are compared in FIGS. 26A and 26B.The new candidate lens is significantly closer to diffraction limitedresolution, has lower chromatism and polychromatic mean square wavefrontdeformation than the actually fabricated lens. It is important torecognize that the resolution of the AWARE-2 imager system includes themicrocamera relay optics. The relay optics corrected for aberrations inthe primary, as well as provided flattening of the relayed image fieldonto the planar image sensors. In fact, the overall AWARE-2 systemoptics design was diffraction limited. However, conducting thesystematic design process on a relatively long focal length system,where geometrical aberrations are influential on resolution, served as asuccessful test of the design methodology.

V.2 F#1.71 12 mm Focal Length Lenses

One exemplary goal was to design an imager with at least 120° field ofview and resolution and sensitivity comparable to the human eye (1 arcminute), resulting in about 100 Megapixels total resolution. Forexample, assuming that the exemplary waveguide configuration of themulti-scale monocentric imager 102 of FIG. 1B is used with 2.5 micronpitch NA=1 fiber bundles, an exemplary goal can be set of a 12 mm focallength lens with diffraction limited operation in the photographicspectral band (0.47 to 0.65 μm) and the numerical aperture of 0.29(F/#1.71). For example, designed was the monocentric lens assuming fiberstop operation mode, which means that the fiber taper shown in theexemplary embodiments 102 and 201 can provide effective light filteringof all rays traveling out of rotated on field angle physical stop. Thedetails on fiber stop operational mode will be given in the followingsection. As that is the more demanding design: the physical aperturestop and vignetting of the field beams will increase diffraction atwider field angles, but can only reduce geometrical optic aberrations.

The result of the design process was an initial evaluation of 198,000glass pair systems, of which some 56,000 candidates passed the initialevaluation and were optimized using exact ray tracing to generate thefinal ranked list. The entire process took only 15 minutes to generateusing single-threaded Matlab optimization code running on a 2.2 GHz i7Intel processor. Part of this list is shown in Table 3. Becausedifferent optical glass manufacturers produce similar glasses thesolutions have been combined in families, and the table shows the firstnine of these families. For example, shown are radii for a primary glassand list several substitutions glasses in parenthesis. Design with thesubstitutions glasses result in small changes in radii but substantiallythe same performance. The table shows the computed polychromatic meansquare wavefront deformation, the criterion for the analytical globalsearch, and the value for the MTF at 200 lp/mm (Nyquist sampling) foundfollowing Zemax optimization of the same candidate glasses. If thedesign process has worked, one could expect that these metrics would bestrongly correlated. FIG. 27 illustrates by showing the correlation forrepresentative samples of the top 200 solutions, and found is theidentical sequence for all 200 of the top candidates.

TABLE 3 Top solutions for a F#/1.7 f =12 mm monocentric lens. InternalGlass Fast exact ZEMAX radii MTF Outer (substitution glasses ray-tracing(mm) at 200 # Glass shown in parentheses) R1 R2 (ΔΦ)² R1 R2 lp/mm 1S-LAH79 K-LASFN9 (TAF5, S-LAH59) 9.049 3.765 0.0038 9.068 3.792 0.65 2N-LASF46A M-TAF1(MC-TAF1, TAF5,S- 9.057 3.614 0.0041 9.062 3.626 0.61LAH59, K-LAFK50) 3 TAFD40 M-TAFD305 (LAF2, S-LAM2) 9.533 3.729 0.00479.537 3.735 0.59 4 K-GIR79 M-TAF1 (K-LaFK50T) 9.392 3.404 0.0048 9.4013.426 0.59 5 S-LAH79 S-LAL59 (K-LaKn12, TAC4, 8.049 3.772 0.0059 8.0743.807 0.59 TAF4, N-LAF21, TAF1, S- LAH64) 6 S-LAH79 K-VC80 (S-LAL13, M-7.581 3.738 0.0070 7.593 3.756 0.55 LAC130, P-LAK35, LAC13) 7 K-PSFN2N-LASF45 (N-LASF45HT, S- 8.871 3.773 0.0077 8.901 3.819 0.59 LAM66) 8K-PSFN203 BAFD8 (S-BAH28) 7.869 3.769 0.0083 7.886 3.791 0.54 9 P-SF68BAFD8 (S-BAH28) 7.917 3.765 0.0091 7.934 3.787 0.53

The best performance monocentric lens solution (family number 1)demonstrates near diffraction limited resolution over the photographicvisible operational waveband (e.g., 470-650 nm). It uses S-LAH79 for theouter shell glass and K-LASFN9 for the inner glass. To provide a centralaperture stop, it is necessary to fabricate the center lens as twohemispherical elements. Because optical glass K-LASFN9 has a highrefractive index of 1.81, the interface between the two hemisphericalelements can cause reflections at large incidence angles unless theinterface is index matched, and the index of optical cements is limited.For example the Norland UV-cure epoxy NOA164 has an index of 1.64. Thisresults in a critical angle of 65°, and a maximum achievable field ofview of ±55°. For this glass system, it is preferable to fabricate thecenter lens as a single spherical element and operate the system in the“virtual iris” mode, where the system can provide a maximum field ofview of ±78.5°. The optical layout, MTF and ray fan diagrams of the topsolution operating in “virtual” stop mode are shown in FIG. 28.

Table 4 shows the detailed optical prescription of the monocentric lensexample. The lens operation is shown in three configurations. Thedistance to the object plane is changed from infinity to 1 m and then to0.5 m. The back focal distance (e.g., thickness 5 in Table 4) is changedas well. The back focal distance for object at infinity is 2.92088 mm,for 1 m object distance 3.06156 mm and for the 0.5 m object distance3.20050 mm.

TABLE 4 Optical prescription for refocusing of the monocentric lens,showing multiple configurations for three object distances Semi- SurfaceType Radius Thickness Glass Diameter OBJ Standard Infinity 1.0E+10/1000.000/ 500.000 1 Standard 9.06762 5.27607 S-LAH79 9.06000 2 Standard3.79155 3.79155 K-LASFN9 3.79000 STO Standard Infinity 3.79155 K-LASFN91.94188 4 Standard −3.79155 5.27607 S-LAH79 3.79000 5 Standard −9.067622.92088/ 9.06000 3.06156/ 3.20318 IMA Standard −12.2708 — 11.0000

The MTF for two extreme object positions is shown in FIGS. 29A and 29B.After refocusing to closer object distance, the image surface losesconcentricity with the lens but still retain the original radius, as wasshown in Section III. The loss of concentricity enables conjugationbetween planar objects at a finite distance to the spherical imagesurface, and so implies the ability to focus onto points anywhere in theobject space. A concentric system designed at a specific finite objectradius can be conjugated only with a specific concentric spherical imagesurface, and focus of a concentric lens system onto spherical objects atdifferent distances would require the change in the image surfaceradius. At closer object distances, angle α₁ (FIG. 23) increases fromzero to some small finite value, which changes spherical aberration (Eq.(10)) and MTF slightly away from optimum value. As predicted by thirdorder aberration analysis, image quality can be maintained close to theoriginal infinite conjugate design during refocusing operation, over awide range of field angles. A ZEMAX design files modeling this lens areavailable for download at http://psilab.ucsd.edu/VirtualStopFamily1.zip.Note that adequate simulation of the “virtual stop” operational mode inZEMAX requires the rotation of the aperture stop at off-axis fieldangles, as well as rotation on this angle image surface around itscenter of curvature. In this file, a distinct configuration has beendefined for each field angle.

The members of the family six of Table 3 have a glass with asignificantly lower refraction index of the central glass ball, 1.69,which can be index matched with standard UV cure epoxies. This enablesthe lens to be fabricated as two halves, and assembled with a physicalaperture stop at the center. While members of this family have slightlylower image quality performance they can fully operate over ±65° fieldof view in both “virtual” stop and “aperture” stop modes. The opticallayout, MTF and the ray fan diagrams of the top member of the thirdfamily operating in the “aperture stop” mode for the object located atinfinity is shown in FIG. 30. The ray fan graphs are shown for the axialand 60° field points at the image surface. The scale of ray fans is ±10μm. The design has been modified to include a 10 μm thick layer ofNOA164 glue between the two glasses, and in the central plane.Simplified ZEMAX files of this lens without optical cement are alsoavailable at: http://psilab.ucsd.edu/PhysicalApertureStopFamily3.zip

The optical layout 3301 and MTF of the top member of the family numbersix operating in the “fiber stop” mode is shown in FIG. 30. The“virtual” stop mode has a uniform high image quality performance allover the field. The “aperture” stop mode suffers from drop inperformance at the edge of the field due to the pupil vignetting andaberrations in the optical cement layer. This design is useful, however,as operation in the “aperture” stop mode simplifies requirements to theimage transfer and detection. In this case the input aperture of thefiber bundle can exceed back aperture of the optics, as the physicalaperture stop provides all stray light filtering needed, and the imagetransfer can be done with relay optics or with standard Schott fiberbundles with NA=1 and 2.5 micron pitch.

V.3 Comparison with Conventional Wide Angle Lenses

The architecture of monocentric lens is intrinsically compact: theprincipal (central) rays of all field angles are orthogonal to the front(powered) optical surface, and are directly focused to an image surfacewhich is always substantially perpendicular to the incident light.Conventional wide field of view imagers require a lens which conveyswide field input to a contiguous planar image surface. Extreme wideangle “fisheye” lenses use two stage architecture in the more generalclass of reverse-telephoto lenses, where the back focal distance isgreater than the focal length. The front optic in FIG. 31 is a wideaperture negative lens to insure acceptance of at least a fraction oflight incident over a wide angle range. The negative power reduces thedivergence of principal rays of the input beams, so the followingfocusing positive component operates with a significantly reduced fieldof view, although it must provide sufficient optical power to compensatefor the negative first element. This retro-telephoto architectureresults in a physically bulky optic. FIG. 31 shows two conventionalwide-field lenses on the same scale as the f=12 mm design example above.At the top of the FIG. 31 is an element “fisheye” lens taken directlyfrom the Zebase catalog of standard lens designs (F_004), then scaledfrom 31 mm to the 12 mm focal length. The smaller lens at the center ofFIG. 31 is based on the prescription for a 9-element wide field lensspecifically designed to minimize volume. This design was intended for ashorter focal length, and the aberrations are not well corrected whenscaled to 12 mm. When this design was optimized, even allowing asphericsurfaces, the components tended toward the same overall physical shapeand volume of the lens above. Both of these lenses are substantiallylarger than the monocentric lens design, even including the volume ofthe fiber bundles, and they collect less light, even including forcoupling and transmission losses in the fiber bundles. For example,looking further at a specific design example, identified were high- andlow-index center glass solutions for F/1.7 12 mm focal lengthmonocentric lenses with (at least) a 120° field of view, and showed thatthis lens compares favorably to conventional fisheye and projection lenssolutions to panoramic imaging. It is reasonable to ask whether thespecific designs used for the comparison were optimal, and in fact thereis clearly room for improvement in these specific designs. However, thestandard lens categorization shown in FIG. 32 indicates that monocentriclenses can enter a domain of light collection and field of view which isnot otherwise addressable.

V.4 Other Exemplary Two Glass Specific Designs

V.4.1 Compact Monocentric Mass-Productable Cell Phone Camera Lens

FIG. 33 shows an exemplary layout and compact cell phone camera assemblyof the 3 mm focus 120 degrees field of view monocentric cell phone lenshaving the central ball lens made from glass LLF8 and outer shell lensmade from optical plastic-polycarbonate. The optical prescription isshown in the Table 5.

TABLE 5 The optical prescription of the 3 mm focus two glass MC lens.Type Radius Thickness GLASS Semi-Diam. OBJ Standard Infinity Infinity 1Standard 1.9619 1.1385 POLYCARB 1.96 2 Standard 0.8235 0.8235 LLF8 0.823 Standard Infinity 0.8235 LLF8 0.57 4 Standard −0.8235 1.1385 POLYCARB0.82 5 Standard −1.9619 1.09929 1.96 IMA Standard −3.06122 2.9

Another optional design for the exemplary compact 3 mm focus MC lenswith F3=1.71 having optical plastic outer shell is shown in the Table 6.

TABLE 6 The optical prescription of the 3 mm focus two glass MC lens.Type Radius Thickness GLASS Semi-Diam. OBJ Standard Infinity Infinity 1Standard 1.8989 1.1095 POLYCARB 1.81 2 Standard 0.7895 0.7895 FF2 0.7823 Standard Infinity 0.7895 FF2 0.56 4 Standard −0.7895 1.1095 POLYCARB0.782 5 Standard −1.8989 1.07097 1.81 IMA Standard −2.96994 2.57

Both lenses have are operating in the 0.4 μm to 0.7 μm spectral band andgive 0.5 MTF contrast at 200 lp/mm. Such compact lens can bemass-producible in two exemplary steps. For example, at the first step,the glass ball lenses can be manufactured with rolling technology. Atthe second step, the glass balls can be mounted into the mold of theouter plastic lens. The plastic melt temperature can be configured to bearound 150° C., which is one order of magnitude less than glass melttemperature, e.g., which is around 1500° C. So molding of theplastic-glass sandwich at the second step will not damage glass ball.The outer to the glass core plastic lens can be molded together with theattachment mechanical trusses (armature block 3331 in the FIG. 33).After the molding, the assembly of the monocentric lens can be preparedwith plastic camera housing. The assembly 3330 is shown in the FIG. 33.For example, refocusing of the exemplary 3 mm focus monocentric lens canrequire an axial shift of the lens of 0.09 mm. This is the differencebetween back distances numbered as 32 and 24. Such shift can be madewith the inexpensive coil motor 3332. The motor will push thelens-housing connector trusses (armature beams), as shown in FIG. 33.Thus with this technology the whole cell phone refocusable objectiveassembly can be mass-producible with the cost as low as $1.

As was shown in the Section II, this exemplary imager assembly can berefocused in a wide range of the object distances. With refocusing fromthe infinity object distance to the 100 mm distance the back focaldistance changes from 1.09929 mm to 1.19292 mm. The condition of Eqs.(3) and (4) for astigmatism and image curvature do not change. So thesystem will be still free from the third order astigmatism and will keepthe radius of the image surface. However angles α_(i) in Eq. (11) willchange and third order spherical aberration begins to grow up. Becauseby operating with the physical aperture stop, the entrance pupil at thefield points gets elliptical shape, e.g., such cut off of the sphericalaberration in tangential plane deceptively transfers this sphericalaberration to the additional astigmatism. Nevertheless if this variableis compensated over the focusing distance spherical aberration, theassociated field astigmatism is compensated as well. The variablespherical aberration can be compensated with modified spherical Alvarezlens. As shown in FIG. 35, two (rotated in opposite directions)concentric meniscus 3801 and 3802 can be mounted in front of themonocentric lens. The concentric meniscuses 3801 and 3802 can beconfigured to have the aspherical deformation, e.g., which depends onthe angles φ_(x) and φ_(y) between system axis and the vector connectingthe point on the surface with the center of the curvature. Asphericaldeformation S(φ_(x),φ_(y)) will beA*(6φ_(x) ⁵/5+4φ_(x) ³φ_(y) ²+6φ_(x)φ_(y) ⁴−6φ_(x)φ_(y) ²−2φ_(x)³)  (39)for the first surface and−A*(6φ_(x) ⁵/5+4φ_(x) ³φ_(y) ²+6φ_(x)φ_(y) ⁴−6φ_(x)φ_(y) ²−2φ_(x)³)  (40)for the second one. With rotation on the angle Δφ_(x) of the firstmeniscus and on the angle −Δφ_(x) the second one will have variablethird order spherical deformationΔS(φ_(x),φ_(y))=2*A*Δφ _(x)*[6(φ_(x) ²+φ_(y) ²)²−6(φ_(x) ²,φ_(y)²)+1]  (41)

FIGS. 34 and 35 shows the monocentric lens having the mounting meniscusand refocused from infinity to close distance with rotated Alvarez lensaberrations compensator. FIG. 34 shows a diagram of an exemplary compactmonocentric lens with neutral spherical Alvarez lens aberrationcompensation, e.g., shown by components 3701 and 3702, positioned toprovide no optical power. FIG. 35 shows a diagram of an exemplarycompact monocentric lens with active spherical Alvarez lens aberrationcompensation, positioned to provide optical power. For example, themonocentric optical imaging modules shown in FIG. 34 can include twooptical elements 3801 and 3802 having complementary phases to form anAlvarez lens for close focusing operations.

V.4.2 Compact Monocentric Mid Infrared Imager

The next embodiment 3900 of the two glass monocentric lens is designedto operate in the MWIR (3 μm to 5 μm) waveband. The outer opticalmaterial 3901 is ZN Selenide. The internal ball optical material 3902 isAGCL (silver chloride) cristalline compound. The layout of the lens isshown in FIG. 36. The refraction index of the AGCL cristal is in therange of 2. The MWIR optical cement Arsenic-doped amorphous selenium hasrefraction index 2.5. So the lens can operate over whole wide field ofview without total internal reflection at the flat cement layer of thecentral ball. Hence it can successfully operate in the aperture stop andfiber stop mode. This lens operates with F#=1.5. The opticalprescription of the MWIR monocentric lens is shown in Table 7.

TABLE 7 The optical prescription of the MWIR two glass MC lens. TypeRadius Thickness GLASS Semi-Diam. OBJ Standard Infinity Infinity 1Standard 10.0488 5.94728 ZNS_BROAD 10 2 Standard 4.10158 4.10158 AGCL 53 Standard Infinity 4.10158 AGCL 2.0293 4 Standard −4.10158 5.94728ZNS_BROAD 5 5 Standard −10.0488 1.93327 10 IMA Standard −11.98212 10.37

The MTF of the lens operating in the aperture stop mode is shown in FIG.37 All embodiments of the 12 mm focus monocentric lenses together withreceivers assembly have size of about 23 mm. To deliver the image fromthe intermediate spherical image surface to the receiver thechalcogenide fiber bundle can be used. For example, a receiver arraythat can be used TACHYON uncooled MWIR array, e.g., from New IRTechnologies. The TACHYON FPA sensors, made of polycrystalline PbSeusing the Vapor Phase Deposition manufacturing method (exclusive fromNIT), are built directly on top of the Si-CMOS readout circuitry (ROIC)taking advantage of the VPD-Si-CMOS manufacturing method compatibility.This allows the use of large Si-CMOS substrates (8-inch) and has a bigimpact in the final cost per device obtained. The spectral response ismainly centered in the MWIR (3-5 μm) with a peak response at 3.7 μm; inaddition, the material has an extended response down to 1 μm.

V.4.3 Compact Monocentric LWIR Lens

The optical prescription of the compact 12 mm focus Long Wave InfraredMC lens is shown in the Table 8.

TABLE 8 Optical prescription of the compact LWIR MC lens Type RadiusThickness GLASS Semi-Diam. OBJ Standard Infinity Infinity 1 Standard11.0465 6.30297 GERMANIUM 10 2 Standard 4.74349 4.74349 CDTE 5 3Standard Infinity 4.74349 CDTE 2.0293 4 Standard −4.74349 6.30297GERMANIUM 5 5 Standard −11.0465 0.89959 10 IMA Standard −11.94606 10.37

The lens is operating in the waveband 8 to 12 microns. The working F# ofthe lens is 1.6. Lens has diffractional image quality.

VI. Monocentric Lens Imagers Capable to Operate in Extended Wavebands

In the Section IV of this patent document, a combination of Seidel3^(rd) order aberration analysis was used with exact ray-traceoptimization to achieve a fast global search of two glass symmetric(2GS) geometries for a given focal length, F-number and waveband ofinterest. Since the number of degrees of freedom was 3, a direct checkof all 312,000 possible glass combinations (using the entire availableglass catalog) yielded a one-dimensional optimization, which could beexecuted within minutes. Such search for the two glass MC lens solutioncan gave diffractional limited results for the F# above 1.7 andphotographic spectrum band with wavelengths from 0.47 to 0.65 microns.Moreover the use of photographic operational spectrum band required touse the complex band pass filter. To apply such filters to anyhemispherical optical surface of the MC lens raise a significanttechnological challenge. So this coating has to be applied on theentrance surfaces of image delivery fiber bundles thus increase the costof overall assembly. While two glass MC lenses are still attractivesolution for the low cost compact wide field of view imagers the opticalsolutions that can operate in whole wavebands for assigned receivers,for example that can cover 0.4 to 1.05 microns band of front illuminatedCCD, can help to avoid the use of complex coatings and achieve evenhigher light collection power. Requiring a broader spectrum band and alower F-number quickly drove the 2GS geometry to its limits, so the samebasic algorithm was modified to work with a three glass symmetric (3GS)geometry.

In the exemplary 3GS geometry there are around 170 million glasscombinations, and the optimization problem is inherentlytwo-dimensional. For example, in an attempt to reduce the computing timeto reasonable limits, an interesting fact about 3GS geometries wasidentified and made use of. In the 2-dimensional optimization space ofthe three glass symmetric system, if the glass choice is viable, areasof minimum merit function (high performance) look like a long and nearlylinear ravine. So it was possible to fix the radius of second glassshell to some reasonable value, and trade the two-dimensionaloptimization problem for one-dimensional track along the ravine. Thisincreased the computational efficiency and made it possible for theglobal search to run in 24 to 48 hours on a high performance workstation(4×2.7 Hz Intel Xeon E5-4650). The freedom to choose the second radiusin 3GS system was helpful in avoiding excessively thin shells solutions,which are impractical to fabricate. Unfortunately, the 3GS geometryoffered only modest performance improvements, and introducing additionallayers of glass did not provide significant improvement.

A useful solution is to break the front/rear symmetry and introducing anasymmetric air gap between the crown and flint glass core. Introducingsuch an air gap is a common method used for control of spherochromatism.This approach yields the four glass air gap asymmetric geometries, whichimprove performance on extended spectral bands, larger apertures, andlonger focal length systems. The four glass semi-monocentric lensarchitecture 4100 is shown in FIG. 38. For any particular glasscombination the optimization criterion is based on fast exact analyticalray-tracing. The similar to the shown above in Eqs. 15-28 procedure forray tracing the arbitrary ray with entrance height h givessin α₁ =h/r ₁  (42)From the Snell's lawsin α₁ ′=h/(r ₁ n ₂)  (43)From triangle OAB

$\begin{matrix}{{\frac{r_{2}}{\sin\;\alpha_{1}^{\prime}} = \frac{r_{1}}{\sin\;\alpha_{2}}}{or}{{\sin\;\alpha_{2}} = \frac{h}{\left( {r_{2}n_{2}} \right)}}} & (44)\end{matrix}$Then from Snell's law

$\begin{matrix}{{\sin\;\alpha_{2}^{\prime}} = {\frac{n_{2}\;\sin\;\alpha_{2}}{n_{3}} = \frac{h}{r_{2}n_{3}}}} & (45)\end{matrix}$From triangle OBCα₃=α₂′  (46)Then from Snell's law

$\begin{matrix}{{{n_{4}\sin\;\alpha_{3}^{\prime}} = {n_{3}\sin\;\alpha_{2}^{\prime}}}{or}{{\sin\;\alpha_{3}^{\prime}} = \frac{h}{r_{2}n_{4}}}} & (47)\end{matrix}$Next step from triangle OCD and sine low, one has

$\begin{matrix}{{\frac{r_{3}}{\sin\;\alpha_{3}^{\prime}} = \frac{r_{2}}{\sin\;\alpha_{4}}}{or}{{\sin\;\alpha_{4}} = \frac{h}{r_{3}n_{4}}}} & (48)\end{matrix}$Then from Snell's law

$\begin{matrix}{{\sin\;\alpha_{4}^{\prime}} = {{n_{4}\sin\;\alpha_{4}} = \frac{h}{r_{3}}}} & (49)\end{matrix}$From triangle ODE

$\begin{matrix}{{\frac{r_{4}}{\sin\;\alpha_{4}^{\prime}} = \frac{r_{3}}{\sin\;\alpha_{5}}}{or}{{\sin\;\alpha_{5}} = \frac{h}{r_{4}}}} & (50)\end{matrix}$From Snell's law

$\begin{matrix}{{\sin\;\alpha_{5}} = {{n_{5}\sin\;\alpha_{5}^{\prime}} = \frac{h}{r_{4}n_{5}}}} & (51)\end{matrix}$From triangle OEF and sine low

$\begin{matrix}{{\frac{r_{5}}{\sin\;\alpha_{5}^{\prime}} = \frac{r_{4}}{\sin\;\alpha_{6}}}{or}{{\sin\;\alpha_{6}} = \frac{h}{r_{5}n_{5}}}} & (52)\end{matrix}$Then from Snell's law

$\begin{matrix}{{\sin\;\alpha_{6}^{\prime}} = {{n_{5}\sin\;\alpha_{6}} = \frac{h}{r_{5}}}} & (53)\end{matrix}$from triangle OFK segment OK=S is

$\begin{matrix}{{{OK} = {S = {\frac{r_{5}\;\sin\;\alpha_{6}^{\prime}}{\sin\left( {\alpha_{6}^{\prime} - \alpha_{00}} \right)} = \frac{h}{\sin\left( {\alpha_{6}^{\prime} - \alpha_{00}} \right)}}}}{or}} & (54) \\{S = \frac{h}{\begin{matrix}{\sin\left\lbrack {{\arcsin\left( \frac{h}{r_{5}} \right)} + {\arcsin\left( \frac{h}{r_{1}} \right)} + {\arcsin\left( \frac{h}{r_{2}n_{2}} \right)} +} \right.} \\{{\arcsin\left( \frac{h}{r_{2}n_{4}} \right)} + {\arcsin\left( \frac{h}{r_{3}} \right)} + {{arc}\;{\sin\left( \frac{h}{r_{4}n_{5}} \right)}} -} \\{{\arcsin\left( \frac{h}{r_{1}n_{2}} \right)} - {2\;{\arcsin\left( \frac{h}{r_{2}n_{3}} \right)}} - {\arcsin\left( \frac{h}{r_{3}n_{4}} \right)} -} \\\left. {{\arcsin\left( \frac{h}{r_{4}} \right)} - {\arcsin\left( \frac{h}{r_{5}{n\;}_{5}} \right)}} \right\rbrack\end{matrix}}} & (55)\end{matrix}$

The longitudinal aberration L(h) for this ray will beL(h)=S−F  (56)where F is focal length. To form the optimization criterion the resultsof fast exact ray-tracing with Eqs. 55-56 are used. The entrance heightsh, of these rays areh _(i) =NA×F×p _(i)  (57)where p_(i) is array of reduced rays heights at the pupil. The array isp=[1.0,0.97,0.88,0.8,0.7,0.6,0.5,0.4,0.05]  (58)

For criterion of optimization C is taken the sum shown in the Eq. (59):

$\begin{matrix}{C = {{\sum\limits_{i = 1}^{9}\;{\sum\limits_{j = 1}^{9}\;\left\lbrack {p_{i}{{L_{j}\left( h_{i} \right)}/\lambda_{j}}} \right\rbrack^{2}}} + \left\lbrack {L_{1}\left( h_{9} \right)} \right\rbrack - \left\lbrack {L_{9}\left( h_{9} \right)} \right\rbrack^{2} + \left\lbrack {L_{1}\left( h_{3} \right)} \right\rbrack - \left\lbrack {L_{9}\left( h_{3} \right)} \right\rbrack^{2} + \left\lbrack {L_{1}\left( h_{1} \right)} \right\rbrack - \left\lbrack {L_{9}\left( h_{1} \right)} \right\rbrack^{2}}} & (59)\end{matrix}$where λ_(j) is wavelength, the first member of criterion C equation is asum of squared lateral aberrations reduced to wavelengths and thefollowing three members are squared chromatic longitudinal aberrationsdifferences at the pupil reduced rays heights 1., 0.88 and 0.05. Thelongitudinal chromatic difference at the reduced pupil height 0.05 is aclassical chromatic focus shift. Pupil points with reduced pupil height1 and 0.88 are critical for the spherochromatism reduction. Foroptimization of any MC lens operating in extended wavebands, ninewavelengths was used. For the MC lenses operating with front illuminatedsilicon CCD the waveband 0.4 to 1.0 micrometers was used. The waveband0.4 to 1.0 micrometers is divided on the eight segments which gives ninewavelengths for criterion calculations. This criterion demonstrated agood correlation with system modulation transfer function quality forall types of MC lenses operation in extended wavebands.

VI.1 Optimization of Four Glasses MC Lenses

In another aspect, an optical imaging system includes a monocentricoptical imaging module having concentric optical surfaces that collectlight in a photographic visible spectrum to form an image on a curvedimaging surface that is concentric with the concentric optical surfacesof the monocentric optical imaging module, in which the monocentricoptical imaging module includes an inner glass ball lens of a spherehaving a low refractive index of K-GFK68, K-GFK60 or S-FPM2 and threeouter glass lens elements of higher refractive indices; one or moreimaging sensors each including an array of optical detectors locatedaway from the imaging surface to receive light representing the imageinitially formed on the curved imaging surface and to convert thereceived light into detector signals; and optical waveguides coupledbetween the imaging surface and the one or more imaging sensors toreceive light from the curved imaging surface and deliver the receivedlight to the one or more imaging sensors.

Implementations of the optical imaging system can optionally include oneor more of the following exemplary features. For example, three outerglass lens elements of higher refractive indices can include P-LASF47,K-GFK68, K-LASFN6, or N-KZFS11. For example, three outer glass lenselements of higher refractive indices can include NBFD11, K-GFK68,K-LASFN17, KZFS12 or N-K5.

In another aspect, an optical imaging system includes a monocentricoptical imaging module having concentric optical surfaces that collectlight in a water transmission spectrum band from 0.38 to 0.55micrometers to form an image on a curved imaging surface that isconcentric with the concentric optical surfaces of the monocentricoptical imaging module, in which the monocentric optical imaging moduleincludes an inner glass ball lens of a sphere having a low refractiveindex and three outer glass lens elements of higher refractive indices,one or more imaging sensors each including an array of optical detectorslocated away from the imaging surface to receive light representing theimage initially formed on the curved imaging surface and to convert thereceived light into detector signals, and optical waveguides coupledbetween the imaging surface and the one or more imaging sensors toreceive light from the curved imaging surface and deliver the receivedlight to the one or more imaging sensors.

Implementations of the optical imaging system can optionally include oneor more of the following exemplary features. For example, three outerglass lens elements of higher refractive indices include TAFD30,N-LAF21, LASF35, or K-GIR79.

In another aspect, an optical imaging system includes a monocentricoptical imaging module having concentric optical surfaces that collectlight in a transmission spectrum band from infrared 0.9 to 1.5 micronsto form an image on a curved imaging surface that is concentric with theconcentric optical surfaces of the monocentric optical imaging module,in which the monocentric optical imaging module includes an inner glassball lens of a sphere having a low refractive index and three outerglass lens elements of higher refractive indices; one or more imagingsensors each including an array of optical detectors located away fromthe imaging surface to receive light representing the image initiallyformed on the curved imaging surface and to convert the received lightinto detector signals; and optical waveguides coupled between theimaging surface and the one or more imaging sensors to receive lightfrom the curved imaging surface and deliver the received light to theone or more imaging sensors.

Implementations of the optical imaging system can optionally include oneor more of the following exemplary features. For example, three outerglass lens elements of higher refractive indices include M-FDS2,K-GIR79, K-PSFN215, or N-SF4.

In another aspect, a method for designing a monocentric optical imagingmodule having concentric optical surfaces that collect light to form animage on a curved imaging surface that is concentric with the concentricoptical surfaces of the monocentric optical imaging module, in which themonocentric optical imaging module includes an inner glass ball lens ofa sphere having a low index and three outer glass lens elements ofhigher refractive indices, in which the method includes: determiningsurface radii of the inner glass ball and three outer glass lenselements for combinations of glass materials for the inner glass balland the three outer glass lens elements to minimize monochromatic andchromatic aberrations; the local optimization method will come somewhereinside the thin pancake shaped area of low criterion value solutions,then at a second step optimization search will follow over the mainravine of the cost function which direction was determined from theminimal absolute Eigen vector of the Hesse matrix at the initial minimumcost function point and locating with number of local optimizations thepoints over this ravine inside pancake shaped area of low value of costfunction; then, at a third step, locating minimums over secondaryravines originated from the primary ravine of cost function with thesame method of traveling over directions of secondary eigen vectors ofthe points over primary ravine with the local optimizations from thesepoints. By investigating the pancake area of low cost function valuewith the square net of ravines the method reliably located the area oflowers cost function value and find location absolute minimum for eachparticular glasses combination.

The starting point for four glass systematic search is to use the corefrom multiple two glass top candidates as seeds for furtheroptimization. The more promising glass K-GFK68 was chosen as a basiccore glass for systematic solution search. Other glasses were replacedin all possible combinations. For each glasses combination the search ofminimum of criterion C (Eq. 59) was performed and the optimized systemgiving the minimum value of criterion C was found. For example, with thechosen glass combination, 5 radii were optimized. Actually, for example,there are seven radiuses in the optical scheme including the imagesurface radius (FIG. 38). But the third radius is equal to the negativevalue of the second radius because the central ball lens supposed to bemonocentric and the image surface radius is bounded to the focus.Attempts to optimize four glasses architecture to the minimum ofcriterion C with ZEMAX software shows the number of linear combinationsbetween optimization parameters or in the other words lines and surfacesin the optimization space over which the criterion does not change orchanges very slow. Such areas are multidimensional ravines or saddletype stationary areas. For each glasses combination the minimum of thecriterion C is located at different position in the radiuses space.Nevertheless all glasses combinations have the very common shape ofsolutions area in the 5D radiuses space. For every glasses combinationsif we will draw the contour surfaces with the equal values of criterionC the minimum will looks as a thin pancake in the 5D radiuses space.This thin pancake is pierced with net of saddle type ravines areas. Theoptimization of such kind of functions creates problems for theuniversal methods of optimization such gradient or Newtonians methodsused in commercial lens design software. Optimization methods aredemonstrating the low convergence speed and usually are stuck in thesaddle type ravines still not reaching the minimum. The behavior of thegradient method in such cases is illustrated in FIG. 39. On thegraphical illustration 4201 of gradient method behavior in the generalcase of the normal minimums shape the gradient descend direction at anystep is directed in the orthogonal to the criterion contour line andstraight descend is continued up to the point when it reaches anothercontour line at low value of criterion, e.g., of which the direction ofdescent will be tangential. The process converges fast enough to theminimum in the several steps. In the case of degraded (stretched)minimum with the strong linear dependence between optimizationparameters which is shown in the graph 4202 the gradient method beginsto oscillate. Some methods include the use of conjugated gradients. Itwas shown that apexes of segmented lines in the gradient method arelocated around the line showing the direction to the minimum and afterseveral steps we can create this medium line by using least squaremethod. The move along this line will facilitate the fast descend to theminimum. While method of conjugated gradients can help in number ofdegraded minimums cases, the exemplary situation is more sophisticatedand cannot be illustrated with two dimensional graphics. In theexemplary case, all points inside five dimensional thin pancake minimumarea saddle like points. At every point we have Hesse matrix having onezero Eigen value and Eigen vector demonstrating strong linear dependencebetween the first and last radiuses. This saddle type nature of the areaof minimum is another reason that conventional optimization methods arestuck at different points inside pancake depending on initialoptimization point. In this situation even method of conjugatedgradients failed. The optimization of this lenses architecture requireddevelopment of special methods. This special optimization method will beillustrated on the example of MC lens with the following glasscombination: P-LASF47, K-GFK68, K-LASFN6, N-KZFS11. This exemplaryglasses combination demonstrated excellent performance. The exemplarysearch for the near minimum begins with a gradient descent to theclosest local minimum from the average radii solution for thisarchitecture. The optimization of this glasses combination begins fromthe some average radiuses combination—(7, 2.9, −2.9, −4.2, −4.5, −7.8,−12), where in parentless are shown radiuses of the architecture of FIG.28 in mm's. The local gradient descent method quickly came to the pointwith array of radiuses M1=(7.06457, 2.95860, −2.95860, −4.16102,−4.46400, −7.74390), which again are shown in mm's, and criterion valueat this point is C=0.00709. The contour lines graphs of the criterion C(Eq. (59) in the plane section of radiuses R1-R6 of the 5 dimensionalspace is shown in FIG. 40. The minimum area is thin long strip, which isthe section of five dimensional thin pancake. The minimum point M1 isshown with information box 3202. From the FIG. 40 is clear that this isfootprint of the single minimum finally located somewhere at the area ofR1 having lower value out of the frames of this figure. We used theHesse matrix Eigen vectors to find direction of the strip. The fiveEigen values of the Hesse matrix at this point are: −0.01024, 0.25782,0.91727, 25.44 and 21148.91. Note that radius number three does notparticipate in optimization because it is equal to the negative value ofthe second radius. Two Eigen vectors having smallest Eigen values are:E₁=(−0.6007, 0.00309, −0.00223, 0.00967, −0.79988) and E₂=(0.31650,0.12960, −0.50686, −0.75252, −0.24462), where Eigen vectorsdirectionally cosines are related to the radiuses R1, R2, R4, R5 and R6accordingly. The section of criterion C shows that the main ravine isrelated to the Eigen vector E₁. In FIG. 40 the angle of this ravine withthe axis of first radius R1 measured with protractor is 54.5°. Thedirectional cosine of the Eigen vector E₁ with the axis of the firstradius is −0.6007 shows the angle 53.07°. This is pretty good estimationtaking into consideration that estimation of the direction of slightlynonlinear ravine was made at the small local zone around of point M1. Inthis local zone the increments for the numerical derivatives test wereonly 0.0005 mm. It is a general situation inside optimization space forthis architecture that the minimal Eigen vector E₁ shows the directionwhich demonstrates close to complete linear dependence between the firstand last radiuses of the MC lens. We will name this ravine as the mainvirtual ravine. By knowing that gradient methods are descending in thedirection orthogonal to the contours of equal C values it is notsurprising that gradient methods from any initial point are coming tothe main virtual ravine but to the different location over this ravinedepend on the location of initial point. The 3D graph of the criterion Cwith dependence on the first and last radiuses is shown in FIG. 41. Thevalue of the criterion function C in the direction orthogonal to theravine is quickly reaches value of 0.4 with just such small step inradiuses space as 0.02 mm. We will use the main ravine as an entrancearea into pancake space. We will find several entrance points intopancake stepping over ravine. The main ravine is slightly nonlinear. Soto find new entrances into pancake we need to travel over this straightline which defined by the first Eigen vector direction at the point ofthe founded minimum and make number of local optimizations, which willquickly come to the actual ravine bottoms. Following over the directionof Eigen vector E₁ we made 17 steps with 0.05 increments in the radiusesspace (8 steps in the direction of lower first radius and 8 steps inopposite direction) and making the gradient descent from each point weobtains the array of minimums shown in the Table 9. In the Table 9 isshown the central ten minimums (ravine bottom points) of this scan. Theminimum M1 over the main ravine have number 9 in the Table 9.

TABLE 9 The array of local minimums located over the main ravine. 5 6 78 9 10 11 12 13 14 C_(initial) 0.0132 0.0089 0.0074 0.0071 0.0071 0.00710.0075 0.0092 0.0135 0.022 r1 6.9453 6.9753 7.0052 7.0351 7.0646 7.00957.1252 7.1554 7.1855 7.2157 r2 2.959 2.959 2.959 2.959 2.959 2.959 2.9582.959 2.956 2.957 r3 −2.959 −2.959 −2.959 −2.959 −2.959 −2.959 −2.959−2.963 −2.956 −2.957 r4 −4.162 −4.162 −4.161 −4.161 −4.161 −4.161 −4.161−4.161 −4.161 −4.161 r5 −4.462 −4.462 −4.463 −4.463 −4.464 −4.464 −4.465−4.465 −4.466 −4.466 r6 −7.904 −7.864 −7.824 −7.784 −7.744 −7.704 −7.664−7.624 −7.584 −7.544 C_(final) 0.0072 0.0071 0.0071 0.0071 0.0071 0.00710.0072 0.0073 0.0075 0.0078

Table 9 shows that minimums are located over deep slightly curved ravinewith the strong linear dependence between the first and last radiuses.The local gradient optimization initiated from the points of this linejust make the short descent to this ravine bottom points. Each localminimum located over this main ravine has minimum value eigen vectorwhich is close to be collinear to the vector E₁ at the point M1. Forexample eigen values at the minimum point number 14 in the Table 8 are:(0.0095, 0.252, 1.174, 25.29, 21129.5) and the first eigen vector is:(−0.6245, 0.00681, −0.00823, −0.00390, −0.78094). The scalar product ofthis vector with vector E₁ at the point M1 will be 0.996. So the mainravine is very slightly curved. The body of pancake shaped minimumlocated over the 3D sphera into 5D space and this sphera is orthogonalto the ravine shown in FIG. 40. The directions of the minimum incrementof the criterion C at each bottom point over ravine is direction of thesecond eigen vector while the first one is still directed over ravine.Finally from each minimum at this ravine we investigated the tunnelsinto pancake located over the lines of eigen vectors having the eigenvalue next on the first eigen vectors. This vectors orthogonal to thelocal main eigen vector. The method of pancake structure investigationis the same. With the step of 0.05 mm we initiated local gradientdescents. Actually we investigated thin pancake of criterion C withnumber of local gradient discents initiated from the dense square net ofinitial optimization points. The global minimum for this system wasfound over the tunnel initiated at the bottom point number 7 located atthe main ravine (Table 9). At this bottom point at the main ravine thearray of eigen vectors values are—(0.01185, 0.2590, 0.95738, 25.048, and21154.01). Eigen vector number one is: (−0.58954, 0.00163; −0.00098,0.0129, − 0.8077). First eigen vector is very close to be collinear tothe vector E₁ at the point M1. Eigen vector number two is: (0.312,0.1518, −0.51805 −0.7442, −0.2389). An exemplary strategy includedmaking the search over tunnel associated with secondary Eigen vector.The search was made with 0.05 mm step in the radiuses space. Finally atthe tunnel line associated with eigen vector number two we found theminimum number 3. This minimum has the value of the criterion C equal to0.00387. The array of radiuses at this minimum is: 7.06749, 2.9897,−2.9897, −4.26439, −4.61223, −7.87162. Radiuses are in mm's. This pointwith the minimum value of the criterion C is actually the same typesaddle point as others inside pancake. Eigen values at this pointare—(−0.00726, 0.13978, 0.63353, 21.93178, 17845.4). In the areasurrounding this global minimum the values of criterion C are still low.So we actually have to speak about area of solutions rather than aboutsingle global minimum solution. For example the minimum founded atanother secondary tunnel inside pancake initiated from the minimumnumber 8 (Table 7) at the 3 steps with short gradient optimization hasvalue 0.00388. The array of radiuses in mm's are: (7.09812, 2.98535,−2.98535, −4.26195, −4.61452, −7.83257). The minimum number 3 from theminimum number 6 (Table 9) has criterion value of 0.00393. The array ofradiuses in mm's are: (7.03748, 2.99069, −2.99069, −4.26517, −4.61138,−7.91104). So this area of low value of criterion C is substantiallylarge area inside an exemplary pancake proximately covering patch with0.06 mm size across in the radiuses space. We substituted the array ofradiuses at the point with C=0.00387 into ZEMAX software. The opticalprescription is shown in the Table 10.

TABLE 10 The optical prescription of the optimal solution. RadiusThickness GLASS Semi-Diam. OBJ Infinity Infinity 1 7.06749 4.07771P-LASF47 6.75 2 2.98978 2.98978 K-GFK68 2.96 3 Infinity 2.98978 K-GFK682.2053 4 −2.98978 1.2746 K-LASFN6 2.95 5 −4.2644 0.34785 4.09 6 −4.612243.2594 N-KZFS11 4.37 7 −7.8716 4.1278 7.14 8 −11.9995 11

The optical layout of the lens is shown in the FIG. 42 and opticaltransfer function in the FIG. 43. We loaded the sensitivity of the frontilluminated CCD in the ZEMAX file of Table 10. We constracted ZEMAXmerit function as a function keeping at minimum radiuses of point spreadfunctions at all nine wavelength (operators REAR), maximizing MTF atfrequencies 100, 160 and 200 lp/mm and keeping focal length at 12 mm(operator EFFL). Substitution of the sensitivity of the frontilluminated CCD and quick reoptimization with ZEMAX gave the opticalprescription shown in the Table 11.

TABLE 11 The optitical prescription of the 12 mm focus MC lens operatingwith front illuminated CCD. Radius Thickness GLASS Semi-Diam. OBJInfinity Infinity 1 7.04107 4.08409 P-LASF47 6.75 2 2.95699 2.95699K-GFK68 2.96 3 Infinity 2.95699 K-GFK68 2.2036 4 −2.95699 1.26003K-LASFN6 2.95 5 −4.21702 0.35134 4.09 6 −4.56835 3.30232 N-KZFS11 4.37 7−7.87067 4.12587 7.14 8 −11.99654 11

The image quality is practically diffractional. The MTF of the lens isshown in the FIG. 44. At the 200 lp/mm the lens has 90% level ofresolution from diffractional limit.

The back illuminated CCD are sensitive down to the 200 nm wavelength. Wefound that achromatization in the band of 200 nm to 1050 nm is out ofability of the four glass air gap architecture. So to avoid of the useof expensive coatings we decided to cut off the UV spectrum by using themounting meniscus made from the Schott GG435 absorptive glass. Theoptical prescription of the MC lens operating with the back illuminatedxCCD is shown in the Table 12, where the GG435 color glass is simulatedwith close by refraction index properties N-K5 glass.

TABLE 12 The optitical prescription of the 12 mm focus MC lens operatingwith back illuminated CCD. Radius Thickness GLASS Semi-Diam. OBJInfinity Infinity 1 6.86592 3.92922 NBFD11 6.75 2 2.93671 2.93671K-GFK68 2.96 3 Infinity 2.93671 K-GFK68 2.2036 4 −2.93671 1.27547K-LASFN17 2.95 5 −4.21218 0.36698 4.09 6 −4.57916 2.33722 KZFS12 4.31 7−6.91638 3.07425 6.3 8 −9.99063 2.0000 N-K5 8.8 9 −11.99063 10.4

The MTF of the lens is shown in the FIG. 45. The image quality ispractically diffractional. The optical layout of the lens is shown inthe FIG. 46.

Both lenses have the core glass K-GFK68 with a very high coefficient ofthermal expansion, TCE=12.9, while surrounding glasses have low TCEcoefficients. For example for front illuminated CCD scheme shown in theTable 10 P-LASF47 glass has TCE=6.04 and K-LASFN6 glass has TCE=5.9. Forexample, normally the TCE difference less than 1.5 for cemented surfacescan be recommended for out door optics. Recently, for example, NorlandProducts Inc. offered extremely low psi modulos NOA 76 optical cementwhich can be used for glass pairs with such high CTE differences. ZEMAXthermal modeling of the schemes shown in Tables 10, 11 with 10 micronsthick NOA 76 optical cement shows that lenses can operate in a widetemperature range of −20° C. to +50° C. without image qualitydegradation, just ±0.02 mm back focal length adjustment is required.Because MC lens originally designed to be able for refocusing (SectionII) this procedure does not rise a problem.

Additional families of solutions for the MC lenses operating in theextended spectrum band of back and front illuminated CMOS receivers canbe found with OHARA S-FPM2 glass core ball lens.

VI.2 Compact Underwater MC Lens Imager

Water in the natural reservoirs like ocean nor lakes water contains alot of organic and nonorganic particles and actually are the highscattering media. So the light is fast attenuated and for the imaging ateffective distances underwater optics has to have high light collectionpower. The underwater optics has to operate in specific optical bandshifted to the soft UV spectrum. So the desired operational waveband forunderwater optics is from 0.3 to 0.6 micrometers. Back illuminated CCDsare sensible down to wavelength 0.2 micrometers so principally suchimager operating with whole water transmission band are possible.Additional problem that underwater optics are affected by high pressureon the front lens. Classical wide field optics based on the fish-eye orTopogon shemes have the front meniscus. Finally this high pressureresistance requirements makes classical underwater optics bulky. Forexample, contemporary underwater objectives, e.g., like Gidrorussar 11and 12, have thick cemented doublet in as a front lens and combinesTopogon scheme with Petzval projection lens for distortion compensationand image flattering that makes them complicated and expensive. They canachieve minimum F# of 2. with a 90° overall field. The MC underwaterlens optimized in spectrum band 0.38 to 0.55 microns and have imagespace F#1.79 and can operate with 120 degrees field. The opticalprescription of the four glass with air gap MC lens is shown in theTable 13.

TABLE 13 The optical prescription of the underwater MC lens. RadiusThickness GLASS Semi-Diam. OBJ Infinity Infinity SEAWATER 1 6.043013.48922 TAFD30 5.7 2 2.55379 2.55379 N-LAF21 2.52 STO Infinity 2.55379N-LAF21 1.86186 4 −2.55379 1.45045 LASF35 2.51 5 −4.00424 0.15550 2.52 6−4.15974 2.61865 K-GIR79 3.95 7 −6.77840 5.26988 6.25 IMA −12.0482810.43

The MTF of the underwater MC lens is shown in the FIG. 47. The MTF have70% value from the diffraction limited MTF. Such wide field, high lightgathering power and high pressure resistance because of the use ofcemented ball lens as a front lens makes MC underwater lens highlycompetitive.

VI.3 Compact Short Wave IR MC Lens Imager

Traditional approach to the night vision devices architecture is basedon the of image intensifiers which operates at the star and moon lightspectrum in the waveband of 0.7 to 0.9 micrometers. Generation III imageintensifiers have circular image input area 18 mm in diameter whichperfectly fit to MC 16 mm focus fiber bundle flat output. The requiredresolution of optics to match the tubes resolution is 70 lp/mm. Whileconventional optics for night vision devises have 40° field and operateswith F#1.2 for a maximum light collection the four glass MC lens canoverstep this requirements. The optical prescription of the MC lens fornight vision goggles was found as result of the systematic similar tothe shown in the Section V.1. The optical prescription of the nightvision lens operating with the Gen. III tubes is shown in the Table 14.

TABLE 14 The optical prescription of the MC lens for the Gen III imageintensifier based Night vision googles. Radius Thickness GLASSSemi-Diam. OBJ Infinity Infinity 1 12.213 7.2 K-PSFN173 11.73 2 5.0145.014 K-GIR79 4.97 STO infinity 5.014 K-GIR79 3.672 5 −5.014 2.766K-PSFN173 4.97 6 −7.780 0.265 7.36 7 −8.045 5.490 KZFS12 7.5 8 −13.5352.438 12 IMA −15.972 12.8

The lens designed to operate in the waveband 0.5 to 0.9 microns whichcovers the whole spectrum band of Gen III GaAsP photocathode. But thislens can certainly operate in the standard 0.7 to 0.9 microns wavebandas well. The F# of the lens is 1.2 so it will provide excellent lightgathering power over wide 120 degrees field which 3 times overpass thefield of the standard optics. With this field MC lens provides 100 lp/mmresolution. The lens is light weight 40 g only.

Recent research shows that Skylight glow in the SWIR band providesreliable imaging at night time even in the absence of star light. Thisnight sky glow is due from chemical luminescence in the upperatmosphere. The glow is result of the emission of hydroxyl radicalstransitioning from exited rotational and translational states to lowerenergy states and emitting SWIR photons in the process. During the daytime the UV photons strike water molecules and initiate production ofhydrogen and ozone. At night, the hydrogen and ozone recombines. Themolecules then transition to a low energy state and emit SWIR light. Theprocess reliably continues for all night providing high level of theSWIR illumination at the ground level which comparable with the fullMoon illumination. It is important that SWIR illumination can penetratethe clouds so the night vision in SWIR band does not depend on theweather conditions. For example, wide choices of SWIR cameras areavailable from Sensor Unlimited Corp. For example, Sensor Unlimited SWIRCCDs are uncooled and available in several formats: 640 to 512 or 1280to 1024 pixels. The pitch is 15 μm and it will be reduced in the nearfuture. SWIR cameras are as compact as contemporary visible cameras andthe use of SWIR sensors in MC lens assembly does not show up anyproblems so far. The systematic search of the SWIR lens results in theoptical prescription shown in the Table 15.

TABLE 15 The optical prescription of the MC SWIR lens. Radius ThicknessGLASS Semi-Diam. OBJ Infinity Infinity 1 9.64853 6.08158 M-FDS2 9.23 23.56694 3.56694 K-GIR79 3.54 STO infinity 3.56694 K-GIR79 2.7875 5−3.56694 2.13160 K-PSFN215 3.54 6 −5.69694 0.20974 5.4 7 −5.908284.27312 N-SF4 5.55 8 −10.18140 1.79011 9.05 IMA −11.97151 10.36

The lens has focal length 12 mm, operational waveband 0.9 to 1.5 um andF#1.19 so it will provide an excellent light gathering power. The MTF isshown in the FIG. 48. SWIR MC lens provides close to the diffractionalresolution at 200 lp/mm and hence can operate with CCDs having 2.5microns pixel pitch. Contemporary SWIR sensors like 1280 by 1024 SensorUnlimited have 15 microns pitch. So MC optics will provide advancedimaging even for next generation SWIR cameras. The layout of the lens isshown in the FIG. 49. Lens weight is only 15 g so it can state the faircompetition for the existing wearable night vision optics.

VII. Monocentric Lens with a “Virtual” Stop as a Unique Solution forHigh Gain Panoramic Imagers with Uniform Field Illumination

VII.1 Introduction

Imagers that require the combination of wide field of view, high angularresolution, and large light collection present a difficult challenge inoptical systems design. For example, conventionally fish-eye and Tessarsobjectives are used in wide field of view imagers. Both schemes aresuffering of low gain (ratio between entrance pupil and lens diameters)and significant reduction of resolution and image illumination at theedge of the field. For example, the vital modification of the frontcomponents in Tessar scheme can result in double fold growth of entrancepupil at the edge of the field. The disclosed technology can result inthe developing of the Russar lenses family widely used in theprofessional, underwater and aero photography. Nevertheless Russarlenses are still suffering from the cosine in power three filedillumination reduction. The problem of resolution and field illuminationreduction toward the edge of the field in the panoramic imagers can besolved with implementation of monocentric lenses (MC). MC lenses useonly hemispherical or spherical surfaces that share a single center ofcurvature. This symmetry yields zero coma and astigmatism overhemispherical image surface and on that surface provides a field of viewlimited only by vignetting from the central aperture stop. The challengeof optical design of MC lenses operating in different wavebands fromsoft UV to the MWIR was addressed in the above sections. In the abovesection of this patent document, an effective way of systematicmonocentric lenses design was described, e.g., which found lowaberration solutions for a panoramic lenses having 1 arc minutesresolution over up to 160 degrees field. The last left over problem ofsuch imagers was the reduction of image illumination due to cosineprojection of the aperture stop on the input beams over the field. Whilethis cosine image illumination reduction (in the case of generallandscape imaging) is significant better rather than in best Russarlenses where this image illumination reduction follows by cosine inpower three low this is still a problem which has to be solved. Forexample, some techniques can use MC lenses without the physical aperturestop at the center and use fiber bundles-tapers with restrictednumerical aperture to cut off aberrated rays. Such imagers operatingwith the “virtual” aperture stop will have high resolution uniformillumination over whole field of view. In this report the property ofthe “virtual” stop aberrated light filtering are considered in details.

VII.2 Monocentric Lens Operating with “Virtual” Aperture Stop

Table 4 shows the optical prescription of exemplary top solution of twoglass MC lens operating in 0.47-0.65 micron waveband, having 12 mm focusand F#=1.715. In FIG. 28 is show the layout of the lens operating withthe “virtual” stop over +/−80 degrees field. Or in other words this lenshas not physical aperture stop located at the center. Rays having backaperture exceeding the designed NA are filtered out within the receiverassembly. Such receiving assembly can be array of finite NA aperturefiber bundles-tapers with attached CCD imager. The layout 201 of the MCimager operating with “virtual” stop is shown in FIG. 2. Fiber bundlesplays an important role of delivering image from the spherical imagesurface to the conventional CCD's receivers and filtering out aberratedlight coming through the optical paths out of rotated on the field angle“virtual” stop located at the center of MC lens. In FIG. 28 are shownMTF of this lens calculated with ZEMAX with supposition that image isformatted at the spherical image surface and only rays within back NAaperture 0.292 are reaching the image. The “virtual” stop operation modesolves two important problems. At the first it eliminates the cosinecompression of the imaging beams at the high field angles which wasconsidered as an inevitable “evil” for all wide field lenses operatingwith the physical aperture stop. Such beams compression results insignificant reduction of the illumination and image quality degradationat the edge of the field. To manufacture the physical aperture stop weneed to split the central ball lens in halves, put mask on the one partand cement two parts. The refraction index of the central ball lens is1.81. The optical cements have low refraction index. This results intotal internal reflection at the border of glass-cement for the highfield angles. So the implementation of “virtual” stop is the onlyoperational way for top MC lenses solutions having high central ballrefraction index. Because of the importance of the “virtual” stop modefor the developing of the panoramic imagers having the uniform imageillumination and quality over the wide field of view it optical propertyhas to be detailed investigated. At the exemplary first step, the MClens themselves can be investigated. An issue to be addressed is whatangles with the normal to the image surface the imaging rays, comingwithin the “virtual” stop, and stray light rays, coming from outside“virtual” stop, are coming. One question includes if they are separatedor mixed. For example, if they are separated, that creates a good basison which the actual “virtual” stop imager can be built. For the deliveryof rays from the spherical image surface to CCDs, fiber bundles can beused with restricted numerical aperture, fiber tapers or other deviceswhich restricts rays numerical aperture. The second question is how goodare real receivers assemblies in providing light filtering.

At the first step of investigation we will consider all rays comingdirectly to the image surface over designed optical path within area atthe center of lens where the rotated “virtual” aperture stop will createthe beam with NA=0.292 as the imaging rays. All other rays will be straylight rays. That can be rays coming to the image surface directly but atthe area out of “virtual” aperture stop. It can be rays created bysecondary reflexes at the MC lens surfaces and coming to the imagesurface over more sophisticated optical path rather than designed forimaging rays. For example, the reflections on the MC lens surfaces inthe front half of the lens may not be considered. These rays will goback into the object space. Surfaces in the back half of MC lens willhave actual reflection-refraction properties. Internal ball lens will beuncoated and external has AC with 0.5% reflection. The MC lens hasphysical aperture stop up to the central ball which exceeds in size the“virtual” aperture stop. The manufacturing of this external physicalstop which exceeds in size “virtual” does not create any technologicalproblems because the outer shell of the ball lens will be in any casemanufactured as two separated meniscus and will leave the space out ofthe central ball to mount this stop. These meniscuses will be cementedwith the central ball to prevent mechanical failure due to thetemperature deformations. In the lens shown in FIG. 28 the aperture stopto the central ball has radius 3.7915 mm. FIG. 22 shows a diagramdepicting monocentric lens real ray trace variables.

In FIG. 22, the ray which is incoming with height h and coming to theimage point I can be the imaging ray or stray ray depend on the height h(inside the entrance pupil or out of entrance pupil). The rays reflectedat the point D are all stray rays.

Consider the direct rays to the image point I. For example, it was foundinvariant φ₁=φ′₄. This is Eq. (22) in this patent document. The anglebetween the direct ray and the normal to the image surface with radiusOI=F (F is focus of the MC lens) is the angle φ₅. So from triangle ODIand sine theorem, one will haveF/sin (φ′₄)=R1/sin (φ₅)  (60)Becausesin (φ′₄)=sin (φ₁)=h/R1  (61)one will getsin (φ₅)=h/F  (62)

It means the linear dependence of the sine of the angle between outputrays and the normal to the image surface on the input height. In otherwords it means that all rays having input height within the “virtual”entrance pupil will have angles with the normal to the image surfaceless than output aperture related to this size of pupil and wise versa.So, what was proved was the opportunity for the perfect stray lightfiltering with the use of the bundles-tapers providing the idealfiltering of the rays having incident angle at the image surfaceexceeding lens NA. Computer simulation in FRED confirms this conclusion.

There can be several candidates for the actual ray filters, which can bedelivered to the CCD plane receivers.

-   (1.) Tapers constructed from the fibers having NA=1. The output of    the taper is connected to the CCD. The input side of the taper is    larger than output. So from Lagrange invariant the NA of the input    side is less than output. The face facets of the fibers will be    orthogonal to the image surface of the MC lens. So all rays having    angles with the normal to the image surface larger than designed NA    will be filtered out. Such tapers are produced by Schott Corp.-   (2.) Fiber bundles with desired NA. At this time such bundles have    low efficiency and excessive internal cross talk. Nevertheless they    can be considered as candidates for the rays filters because in the    future the technology can be improved.-   (3.) The microoptics arrays mounted in the front of delivery    bundles. They will works on the principals of the ideal rays filters    described above.-   (4.) The selective, sensitive to the ray incident angles, dielectric    coatings.

The quality of such filters will be the subject of extended researchefforts which will require application the vector diffraction formalismand fibers mode theory to the rays propagation.

VII.3 Section VII Summary

This section gives a strong theoretical foundation for ability ofmonocentric lenses to operate with the “virtual” aperture stop. It hasbeen shown that panoramic imagers with “virtual” stop monocentric lenswill have the uniform field illumination and will be free of reductionof resolution toward the edge of the field.

VIII. Monocentric Lens Focusing Ability and all in Focus Imaging

Conventional imaging cameras can image one object plane at an idealfocus while other planes at other ranges will be defocused depending onthe distance to the optimal plane. By axially moving the detector withreference to the imaging optics this ideally focused plane will changeits position in the object space. The image formation in the ideallyfocused plane conventionally considered as a convolution of the spaceinvariant point spread function (PSF) and an ideal geometrical image ofthe object. So the Fourier transform (FT) of the image in the localinvariant image plane zone, where the space invariant of the PSF isvalid, is the product of the FT of the geometrical object image and FTof the PSF, namely the modulation transform function (MTF). Thisexplains the blurring of the image with degradation of PSF (growingwider). With degradation of the PSF due to diffraction and aberrations(including defocus) the MTF value is reduced at higher frequencies andhence influences the image FT. The loss of high frequencies result inimage quality degradation, particularly defocus blur. However by knowingthe PSF the image can be computationally deconvoluted and restored inquality up to the certain level. Certainly, for example, we cannotretrieve lost image harmonics located out of the finite spectrum of PSF(MTF borders). But inside the frequency range where the MTF has non zerovalues improvements are possible.

For example, if we will axially move the detector during exposure timethe accumulated all in focus PSFs from the point sources located atdifferent distances and at different field points will not change. Hencethe PSF will be axially space invariant and the image will be a 3Dconvolution of the ideal geometrical image of the object with this 3DPSF. Such images can be deconvoluted in the same way as 2D blurredimages. So generally we can avoid time consuming focusing on the objectof interest. We can just make an axial scan of the detector during theframe exposure time and deconvolute the image.

In the Section III, it was proved that the monocentric lens can berefocused on plane objects by reimaging them onto a sphericalintermediate image surface with a fixed radius. Thus we will haveeverything in focus imaging option which will be very attractive for theMC imagers applications. Normally we have two stages of operationalalgorithm for target detection and recognition. At the first stage thetarget has to be detected, then lens has to be focused on the object.For a well-focused target the recognition can be made. With all in focusoption the detection and recognition can be done in one stage.

IX. Monocentric Lens Specific Advanced Applications

Various existing surveillance systems are designed to combine high lightgathering power with a high resolution over omnidirectional field ofview. Examples of such systems are submarines, armed vehicle, vehiclemounted goggle mapping systems and unmanned ground and marine vehiclesphotonic masts.

X. Exemplary Optical Imaging Systems, Devices, and Methods ofFabrication

Exemplary systems, devices, and methods described below can beimplemented for capturing and forming large high quality images usingmonocentric optical imaging.

In a first example, an optical imaging system includes (i) an imageforming optical system including substantially monocentric opticalsurfaces capable of forming an image onto a substantially sphericalintermediate image surface, (ii) a unit of optical waveguide structureswith waveguide input faces disposed in proximity to the substantiallyspherical intermediate input image surface, and with waveguide outputfaces disposed on a substantially planar output image surface, and (iii)a substantially planar optical sensor array (e.g., on a focal plane)disposed to detect light from the optical waveguide structures.

In some implementations of the optical imaging system, for example, thedetected signal can be digitally processed to reduce the apparentblurring of the image signal resulting from an approximately equaloptical crosstalk between adjacent waveguides, e.g., via deconvolutionwith a uniform kernel to reduce the effect of a constant known blurringamount. For example, the digital processing of the signal can beconfigured to be spatially variant across the aperture of the detectedimage to reduce the apparent blurring of the image signal resulting froma spatially variant optical crosstalk between adjacent waveguides, e.g.,via deconvolution with a spatially variant kernel to reduce the effectof a non-uniform but predictable or measured blurring amount.

In some implementations of the optical imaging system, for example, theoptical imaging system can include, in addition to a first waveguidearray and substantially planar image sensor, one or more adjacentwaveguide array and planar image sensors, where the waveguide inputsurfaces are disposed with a minimal spacing so that the image formed onthe substantially spherical image surface is conducted in nearlycontiguous regions onto two or more substantially planar image sensorarrays.

In some implementations of the optical imaging system, for example, theimage forming optical system is modified to direct light to couple intothe waveguides over a wider range of angles using a uniformtwo-dimensional light angle diffusor structure. For example, an outputsurface of the monocentric optical surface and/or the sphericalintermediate image surface can include light directing structures tooptically couple the light into the waveguides. In some examples, alight diffusor can be implemented, e.g., by roughening the input face ofthe waveguide or the spherical intermediate image surface of the imageforming optical system.

In some implementations of the optical imaging system, for example, theoutput face of the image forming optical system can be configured todirect light to couple into the waveguides over a wider range of anglesusing a substantially concentric light angle diffusor structure, e.g.,such that light diffusion can occur only in the radial direction whichcan avoid excess losses, thereby increasing the optical imaging systemangle range more efficiently than, for example, a random diffusor. Forexample, the light diffusor can be structured to include substantiallyconcentric grooves or ridges on the waveguide input surface and/or thespherical intermediate image surface of the image forming opticalsystem. For example, the disclosed technology includes methods ofstructuring the substantially concentric grooves or ridges including byembossing surface relief features into an isotropic layer.

In some implementations of the optical imaging system, for example, thesystem can include a diffractive structure positioned proximate to thewaveguide input face and including features that are smaller than thewaveguide core, e.g., which can be used to direct the waveguide inputsignal towards the physical axis of the waveguide.

In some implementations of the optical imaging systems, for example, theoptical waveguide structures can be configured such that each waveguidecore has a non-cylindrical core cross section which decreases thedependence of waveguide emission angle on the angle and location ofwaveguide input light signal, e.g., such as grooved or wavy shapedwaveguide cores to increase transmission uniformity and suppress straylight.

In some implementations of the optical imaging systems, for example, theindividual waveguides within the optical waveguide structures can beshaped to align each input waveguide core with the center of symmetry ofthe substantially monocentric image forming system, and to taper from alarger core area to a smaller core area, e.g., to preferentiallytransmit light incident on the waveguide input face within a limitedangle range relative to the waveguide input face.

In some implementations, for example, the the optical imaging system canbe focused by axial translation of some or all of the substantiallymonocentric optical surfaces relative to a fixed unit of opticalwaveguide structures. For example, the optical imaging system canfurther include two or more aspheric optical elements operate to providea controlled focus adjustment by lateral translation and/or rotation.

In a second example, an imaging system includes (i) a primary imageforming optical system which forms an image on a first image surface,and (ii) a unit of optical waveguide structures with the waveguide inputfaces disposed in proximity to the first image surface and with thewaveguide output faces disposed on an output image surface, in which theoptical waveguide structures suppress stray light energy bypreferentially transmitting light incident on the waveguide input facewithin a limited angle range.

In some implementations of the imaging system, for example, thestructure of the waveguide is configured to taper from a larger corearea to a smaller core area, e.g., to restrict the range of light anglestransmitted with low loss from the waveguide input face to the waveguideoutput face. In some implementations of the imaging system, for example,the structure of the waveguide is configured to taper down from a largercore area to a smaller core area, and taper up from a smaller core areato a larger core area, e.g., to restrict the range of light anglestransmitted with low loss from the waveguide input face to the waveguideoutput face, and to control the divergence angle of light emission fromthe output face of the waveguide. For example, the unit of opticalwaveguide structures can be configured as an optical fiber bundle whichhas been tapered to control the input and output angle transmissionproperties of the individual waveguides within the fiber bundle.

In a third example, a method to fabricate a unit of multiple waveguidestructures for substantially monocentric imaging systems includesforming an array of substantially parallel optical waveguides that isfirst tapered to form a narrow waist, then shaped to form asubstantially spherical depression on an input face, such that thewaveguide core near the waveguide input faces are oriented toapproximately align with the center of symmetry of the substantiallymonocentric imaging system.

In a fourth example, a method to fabricate a unit of multiple waveguidestructures for substantially monocentric imaging systems includesforming an array of substantially parallel optical waveguides that isdeformed by heat or pressure to create internal structures where thewaveguide cores near the input face are approximately aligned with thecenter of symmetry of the substantially monocentric imaging system, andthe waveguide cores near the output faces are approximatelyperpendicular to the substantially planar output face. In someimplementations of the method, for example, the method can furtherinclude removing material to form a substantially spherical surface onthe input face, and a substantially planar surface on the output face.

In a fifth example, a method to fabricate a unit of multiple waveguidestructures for substantially monocentric imaging systems includesforming an array of substantially parallel optical waveguides withsubstantially planar input and output faces that is first shaped byremoving material from the input and/or output face, then deformed byheat or pressure to create internal structures where the waveguide coresnear the input face are approximately aligned with the center ofsymmetry of the substantially monocentric imaging system, and thewaveguide cores near the output faces are approximately perpendicular tothe substantially planar output face. In some implementations of themethod, for example, the method can further include removing material toform a substantially spherical surface on the Input face, and asubstantially planar surface on the output face.

In a sixth example, a method to fabricate arrays of waveguide-coupledfocal planes includes attaching an array of substantially paralleloptical waveguides with substantially planar input and output faces toan an array of focal planes fabricated on a shared semiconductorsubstrate, followed by removing material from the input waveguide arrayface to form substantially spherical depressions which are aligned withsome or all of the focal planes, such that the combination of waveguidesand sensor can be singulated by dicing into discrete focal planes withattached multiple waveguide structures.

In a seventh example, a method to fabricate arrays of waveguide-coupledfocal planes includes attaching an array of focal planes fabricated on ashared semiconductor substrate to an array of optical waveguides with asubstantially planar output face and an array of spherical depressionswhich are aligned with some or all of the focal planes, such that thecombination of waveguides and sensor can be singulated by dicing intodiscrete focal planes with attached multiple waveguide structures.

Additionally, the exemplary systems, devices, and methods describedbelow can also be implemented for capturing and forming large highquality images using monocentric optical imaging.

In one example, an optical imaging system can include a primary opticalimaging system including one or more optical elements with substantiallyconcentric and substantially spherical surfaces which form an image on asubstantially spherical image surface, a secondary optical systemincluding multiple closely spaced optical waveguides with Inputapertures near to the substantially spherical image surface, such thatat least a portion of the light collected by the primary optical imagingsystem is coupled into the waveguides and guided to the output of thewaveguides, and one or more substantially planar optical detector arraysarranged to receive and detect at least a portion of the light emittedfrom the output of the waveguides.

In some implementations of the optical imaging system, for example, eachof the secondary optics subsections can be configured as a plurality offiber tapers-receivers assemblies in which fiber tapers provide lightfiltering by the use of fiber transmission characteristics, and thephysical shape of the fiber, to deliberately discriminate betweendesired signal and noise in imaging systems, and selectively block lightfrom reaching the sensor by cutting out all rays coming to theintermediate spherical image surface with the incident angles exceedingthe designed numerical aperture, to deliver the corrected wide fieldimage formed on the intermediate spherical surface to the opticaldetectors, e.g., such as flat CCD, CMOS or FPA receivers, e.g., therebyproviding a “virtual” aperture stop. In some implementations of theoptical imaging system, for example, each of the secondary opticssubsections can be configured as a plurality of fiber bundles receiversassemblies where the fiber bundles delivers the corrected monocentriclens portions of the wide field image formed on the intermediatespherical surface to the optical detectors, e.g., such as flat CCD,CMOS, or FPA receivers.

For example, the fiber tapers of the optical imaging system can beconfigured as dual taper fiber bundle to impose stray light strippingand independently control the light emission angle from the exit face ofthe fiber, e.g., for optimal image sensing. In some implementations ofthe optical imaging system, for example, the fiber bundles head can befabricated by producing tapers with the heat stretching, cuttinghourglass taper in half to have two flat ends, polishing the wide end tosphere orthogonal to the principal rays of MC lens. Techniques forfabricating the fiber bundles include the orientation of the fibers tobe substantially aligned with the direction of signal incidence (e.g.,chief ray angle). In some implementations of the optical imaging system,for example, techniques produce fiber bundles to redirect the angle ofincident light to become substantially aligned with the direction offiber orientation can include using a locally space-variant opticallypatterned reflective, refractive, or diffractive surface. In someimplementations of the optical imaging system, for example, themonocentric lens has no the physical aperture stop, and each ofsecondary optics can include a plurality of fiber tapers receiversassemblies and the restricted tapers NA provides stray light filteringsaid the lens operates with the “virtual” aperture stop.

In some implementations of the optical imaging system, for example, thesystem can further include an electrical signal processor that combinesindividual images from the imaging sensors into a single image. In someimplementations of the optical imaging system, for example, at least aportion of the primary optics section can provide a substantiallyspherical reference surface for alignment of the input surface of thesecondary optical subsection. In some implementations of the opticalimaging system, for example, the primary optics section can includespherical or hemispherical elements. In some implementations of theoptical imaging system, for example, at least a portion the secondaryoptics section can provide lateral mechanical registration of theindividual remaining elements of the secondary sections and detectorsystems. In some implementations of the optical imaging system, forexample, the image can be formed at multiple discrete image regions,each image region corresponding to a field of view captured by acombination of the monocentric primary optics section and a secondaryoptics subsection. In some implementations of the optical imagingsystem, for example, the system can further include a plurality of imagesensing elements positioned at the multiple discrete image regions andconfigured to sense images formed at each of the multiple discrete imageregions. In some implementations of the optical imaging system, forexample, each of the secondary optical systems and substantially planaroptical detector arrays can fit within a conical volume radiating fromthe common point of origin of the primary optics section. In someimplementations of the optical imaging system, for example, the inputface of the optical waveguides or the last surface of the primaryimaging system can be structured with refractive, diffractive, orscattering features to control the angle of light coupling into thewaveguides. In some implementations of the optical imaging system, forexample, the input face of the optical waveguides or the last surface ofthe primary imaging system can be structured with radially symmetricfeatures to direct the light from the primary imaging system to beapproximately coaxial with the waveguide axis.

In some implementations of the optical imaging system, for example, thefocal plane can be configured so that large angle light is absorbed orreflected (e.g., not detected), and use of the focal plane'srestrictions on light transmission angle to act as a stray light filter,or virtual iris, in the optical imaging system.

In some implementations of the optical imaging system, for example, thesize of an exemplary color CMOS sensor pixel can be configured to aquarter of the individual fiber diameter at the bundle-taper output,e.g., thereby providing double resolution of the color image readingfiber bundle-taper resolution.

In some implementations of the optical imaging system, for example, thefiber tapers are configured as hourglass tapers with the head of taperproviding substantially perfect monocentric lens output light couplingand with the curved input part and substantially perfect stray lightfiltering with the hourglass part, e.g., in which both parts can beproduced from high numerical aperture fibers preferably with NA=1. Insome implementations, techniques are provided for fabricating fiberbundles where the orientation of the fibers is substantially alignedwith the direction of signal incidence (e.g., chief ray angle), andwhere the transmission characteristics of the overall structure can becontrolled to limit stray light.

In some implementations of the optical imaging system, for example, themonocentric lens can operate in photographic visible spectrum band andcan be composed from two different glasses in which the outer glass canbe a high index flint glass and the inner ball lens glass can be lowindex crown glass; or, for example, in which glass combinations canprovide diffraction quality aberrations correction, e.g., as exemplifiedin the Table 3; or, for example, in which glass combinations can beconstructed by using glass substitutions of glass combinations, e.g., asexemplified in Table 3, in which substitution glasses are within ±0.03range of value of ND and within ±0.2 range of Abbe number from glassesshown in the Table 3.

In some implementations of the optical imaging system, for example, themonocentric lens can operate in the whole spectrum band of the exemplaryfront illuminated silicon CCD and be composed from four differentglasses, and in which the inner ball lens glass includes low index crownglass K-GFK68, K-GFK60 or S-FPM2, and/or possible glass combinations ofouter shell glasses can be those that are shown in the Table 10, e.g.,but not restricted by these exemplary combinations, and in which theexemplary monocentric lens has as an inherent feature the asymmetric airgap and separated from ball lens meniscus and altogether providingdiffraction quality aberrations correction.

In some implementations of the optical imaging system, for example, themonocentric lens can operate the spectrum band of the exemplary backilluminated silicon CCD and be composed from four different glasses, andin which the inner ball lens glass includes low index crown glassK-GFK68, K-GFK60 or S-FPM2, and/or possible glass combinations of outershell glasses can be those that are shown in the Table 11 and/or 12,e.g., but not restricted by these exemplary combinations, and in whichthe exemplary monocentric lens has as an inherent feature the asymmetricair gap and separated from ball lens meniscus altogether providingdiffraction quality aberrations correction while the mounting fiberbundles-tapers meniscus, e.g., which can be made from GG435 Schott glassor other colored glasses and provides cut of spectrum filteringparticularly down of wavelength 435 nm or anywhere between 425 nm and475 nm.

In some implementations of the optical imaging system, for example, themonocentric lens can operate in the water transmission spectrum band0.38 to 0.55 micrometers and can have water as a first medium and thecentral ball assembly that can be composed from four different glasseswith asymmetric air gap located after the central ball assembly and theouter glass of the central ball assembly including high index flintglass while the inner ball lens glass is low index crown glass with aminor difference in Abbe number between the first and a second glass andstrong difference in Abbe number between second and third glass such asthose exemplified in the Table 13, e.g., but not restricted to thatprescription, and/or other glasses combination following shown aboveglasses combinations rules that are possible.

In some implementations of the optical imaging system, for example, themonocentric lens can operate in the short wave infrared 0.9 to 1.5microns transmission spectrum and can be composed from four differentglasses, in which the outer glass of ball lens assembly can include highindex flint glass and inner ball lens glass including low index crownglass with a strong difference in Abbe number between the first and asecond glass and strong difference in Abbe number between second andthird glass and asymmetric air gap separating the ball lens assembly andlast meniscus such as those exemplified in the Table 15, e.g., but notrestricted to that prescription, and/or other glasses combinationfollowing shown above glasses combinations rules that are possible.

In another example, a method of a systematic search of two glassmonocentric lens optimal aberration correction solution can include, ata first step, for every particular glasses combination optimizing thefirst concentric radius for minimum third order spherical aberrationwhile keeping the second concentric radius bounded to the first radiusand focus length; then, at a second step, optimizing the first radius bymean of minimalizing monochromatic and chromatic aberrations of exactraytraced, e.g., with monocentric architecture methods.

In another example, a method of a systematic search of four glass withasymmetric air gap monocentric lens optimal aberration correctionsolution can include, at a first step, for every particular glassescombination optimizing the first, second, third and fourths concentricradius by keeping the fives radius bounded to the given focal length.Radiuses can be optimized for minimum of monochromatic and chromaticaberrations of exact raytraced, e.g., with monocentric architecturemethods. The local optimization method can come somewhere inside thethin pancake shaped area of low criterion value solutions. Then, themethod can include, at a second step, performing an optimization searchthat will follow over the main ravine of the cost function whichdirection was determined from the minimal absolute Eigen vector of theHesse matrix at the initial minimum cost function point and locatingwith number of local optimizations the points over this ravine insidepancake shaped area of low value of cost function. Then, the method caninclude, at a third step, locating minimums over secondary ravinesoriginated from the primary ravine of cost function with the same methodof traveling over directions of secondary Eigen vectors of the pointsover primary ravine with the local optimizations from these points. Forexample, by investigating the pancake area of low cost function valuewith the square net of ravines the method reliably located the area oflowers cost function value and find location absolute minimum for eachparticular glasses combination.

In some examples, a refocusable monocentric objective assembly includingan monocentric lens system of the disclosed technology can be configuredwith an air image surface or a spherical image surface located on theouter side of a mounting meniscus, a linear motor for the controllableaxial shift of the ball lens assembly regarding receiver assembly, adigital controller for image contrast analysis and generating thedriving signal to the focusing executive said mechanics that altogetherprovides fast autofocusing on the chosen by operator object of interestor automatically on the object which prevail in the size on the imagedscene.

In some examples, a compact (e.g., 4.75 mm in size) refocusablemonocentric imaging lens including a central ball lens including opticalglass and an outer concentric lens including an optical plastic, e.g.,which can be used in the cellular applications.

In some examples, a two stage low-cost mass-production fabricationtechnique to produce an exemplary compact refocusable imager assemblycan include, at a first stage, the use of rolling or molding technologyfor manufacturing of the central glass ball lens and embossing thiscentral ball lens into optical plastic outer shell together with housingarmature used for attachment of the optical assembly to the objectivehousing at a second stage.

In some examples, a compact photonics mast constructed of themonocentric lenses can include 0.5 arc minutes resolution overomnidirectional field with 70 degrees elevation or hemispherical fieldof view and operating in visible, SWIR, MWIR and LWIR wavebandsconcurrently or in any combinations of those wavebands. In someexamples, a compact photonics mast constructed of the monocentric lensescan include 0.5 arc minutes resolution over omnidirectional field with70 degrees elevation or hemispherical field of view and operating invisible, SWIR and MWIR wavebands concurrently or in visible or SWIRwaveband, or just only in visible band, and having close loop connectionto an operator located inside armed vehicle who is equipped with a headtracker and consequently receiving from him the direction to the area ofinterest and real time downloading the foveated image of this localfield to the head mounted display having restricted field of view andcreating an impression of “transparent armor”.

In some examples, a compact UAV imager constructed of the monocentriclenses can include 0.5 arc minutes resolution and having a back loopconnection with a ground operator to receive the direction of theinstant interest and real time download the foveated high resolutionimaging through a restricted capacity communication channel. In someexamples, a compact light weight wearable imager constructed of themonocentric lens can include operating in SWIR waveband to provide viahead mounted display the night vision ability to the dismounted warriorat the outdoor field environment under night glow illumination. In someexamples, a compact light weight wearable imager constructed of themonocentric lens can include operating in NIR waveband to provide thenight vision ability at the outdoor and indoor environment via imageintensifier and head mounted display or via classical night visiondevices equipped image intensifier and eyepieces. In some examples, acompact light weight wearable imager constructed of the monocentriclenses can include operating one lens in NIR waveband and the secondlens in SWIR waveband to provide via head mounted display the nightvision ability at the outdoor and indoor environment concurrently. Insome examples, a compact light weight wearable imager constructed of themonocentric lenses can include operating in MWIR waveband to provide viahead mounted display real time muzzle flashes detection and projectilestracking ability to dismounted warriors or law enforcement personnel. Insome examples, a compact light weight wearable imager constructed of themonocentric lenses can include operating in LWIR waveband to provide viahead mounted display or via compact photonic mast the real time longwave infrared thermal imaginaries to dismounted warriors, armed vehiclepersonnel or law enforcement personnel.

In some examples, a compact persistent surveillance system includingmonocentric lenses of the disclosed technology can be operated invisible, NIR and SWIR optical wavebands or in any combinations ofwaveband and can be equipped with video controller to automaticallyselect objects of interest, e.g., like a moving objects but notrestricted to such requirements, and able to download the compressedhigh definition imageries to the data storage device for adistinguishable time or to download real-time foveated high resolutionand definition imageries to the operator.

In some examples, a light weight Gigapixel-capacity photo camera orcamcorder can include the disclosed optical imaging monocentric lens. Insome examples, a compact high resolution imager constructed from themonocentric lens can include, mounted at the back of a car or track,delivering of an image around the back hemisphere space behind thevehicle to the dash board or head up display. In some examples, awearable augmented reality system constructed from the monocentric lenscan include a wide field of view head mounted display and computercontroller which delivers through computational optics procedures to adismounted warrior, law enforcement personnel, or whoever is in needimageries of a battle field scene or potentially dangerous environment,including but not restricted to, the zoomed images of objects ofinterest, automatically selected threats, all in focus imageries overwhole depth of field, inhaled color imageries for camouflaged objectsdetection and other information. In some examples, a wearable augmentedreality system constructed from the monocentric lens can include,operating in the SWIR spectrum waveband, a wide field of view headmounted display and computer controller which delivers to provide a firefighter with computational optics imagery of the surroundings in the lowvisibility conditions of the smoke and fire, including but notrestricted to, the zoomed images of objects of interest, all in focusimageries over whole depth of field, maps of the building interior andother information. In some examples, a compact and light weight cameraconstructed from the monocentric lens can include mounting on asportsmen's head to deliver real time imaginary for the broadcastingduring sport completions or to the trainers and advisors for sportsmenperformance analyzing or his or her personal records. In some examples,an unattended ground sensor or buoys equipped with compact and lightweight omnidirectional photonic mast constructed from monocentric lensescan include persistent surveillance which delivers a real time imageryor accumulate and periodically downloads these imageries of theenvironment to the operational team through a restricted capacitycommunication channel. In some examples, a compact and light weightcamera including a monocentric lens system of the disclosed technologycan be mounted on K-9 dogs that can be used during a criminal scenesearch or rescue operation, e.g., into areas like debris or narrow tubesin which human personnel have restricted access to deliver a real timeimagery of the environment to the operational team through a restrictedcapacity communication channel.

In some examples, a refocusable monocentric objective assembly caninclude a monocentric lens system including air image surface orspherical image surface located on the outer side of the mourningmeniscus, the linear motor for the controllable axial shift of the balllens assembly regarding receiver assembly, digital controller for imagecontrast analysis and generating the driving signal to the focusingexecutive said mechanics that altogether provides fast autofocusing onthe chosen by operator object of interest or automatically on the objectwhich prevail in the size on the imaged scene.

In some examples, refocusable monocentric objective assembly can includea receiver assembly that is mounted on the basic negative menus lens orspherical image surface that can be located in the air and objectivemonocentric optics that include the rotational Alvarez lens forcorrection of variable over refocusing band spherical aberration andconcurrently correction of associated with this spherical aberrationfield astigmatism, which is due to the vignetting at the objectivefields points. In some implementations, for example, the assembly caninclude Alvarez lens having two concentric meniscuses with asphericaldeformation providing compensation of variable spherical aberrationsover close to hemispherical field of view by rotating meniscuses in oneplane in opposite direction on prescribed angles associated with valueof compensated aberrations at the associated focusing distance.

In some examples, a method to demonstrate the focusing possibility of amonocentric lens or lenses, which can be applied to the all possiblescaled up and down embodiments of lenses and lead to the design of theassociated modified variable rotational Alvarez lens correctorsdifferent from exemplary variable spherical aberration corrector. Forexample, while the variable spherical aberrations correctors can besufficient for the exemplary monocentric lenses embodiments having focallength in the frames of 3 to 12 mm and refocus distances from infinitydistance to the distance of 50 mm, other exemplary sophisticatedcorrectors can be designed based on the aberrations correction methodfor the architecture of the lenses having focus larger or less, e.g., ascompared to other examples previously described, or for the focusingranges closer than other examples previously described.

In some examples, an imager can include a monocentric lens and mechanismto provide focusing using axial translation of the monocentric lensduring the optical exposure, which is capable of acquiring an image thatcan be digitally processed to extend the depth of focus, or to removeartifacts in the image from defects or seams which would be visible inthe directly sensed in-focus image.

In some examples, an imager can include a monocentric lens and mechanismto provide focusing using axial translation of the monocentric lensduring the optical exposure, which is capable of acquiring an image thatcan be digitally processed to get sharp images of the objects locatedwithin the whole range of refocusing, e.g., “all in focus” imaging.

Implementations of the subject matter and the functional operationsdescribed in this patent document can be implemented in various systems,digital electronic circuitry, or in computer software, firmware, orhardware, including the structures disclosed in this specification andtheir structural equivalents, or in combinations of one or more of them.Implementations of the subject matter described in this specificationcan be implemented as one or more computer program products, i.e., oneor more modules of computer program instructions encoded on a tangibleand non-transitory computer readable medium for execution by, or tocontrol the operation of, data processing apparatus, The computerreadable medium can be a machine-readable storage device, amachine-readable storage substrate, a memory device, a composition ofmatter effecting a machine-readable propagated signal, or a combinationof one or more of them. The term “data processing apparatus” encompassesall apparatus, devices, and machines for processing data, including byway of example a programmable processor, a computer, or multipleprocessors or computers. The apparatus can include, in addition tohardware, code that creates an execution environment for the computerprogram in question, e.g., code that constitutes processor firmware, aprotocol stack, a database management system, an operating system, or acombination of one or more of them.

A computer program (also known as a program, software, softwareapplication, script, or code) can be written in any form of programminglanguage, including compiled or interpreted languages, and it can bedeployed in any form, including as a stand-alone program or as a module,component, subroutine, or other unit suitable for use in a computingenvironment. A computer program does not necessarily correspond to afile in a file system. A program can be stored in a portion of a filethat holds other programs or data (e.g., one or more scripts stored in amarkup language document), in a single file dedicated to the program inquestion, or in multiple coordinated files (e.g., files that store oneor more modules, sub programs, or portions of code). A computer programcan be deployed to be executed on one computer or on multiple computersthat are located at one site or distributed across multiple sites andinterconnected by a communication network.

The processes and logic flows described in this specification can beperformed by one or more programmable processors executing one or morecomputer programs to perform functions by operating on input data andgenerating output. The processes and logic flows can also be performedby, and apparatus can also be implemented as, special purpose logiccircuitry, e.g., an FPGA (field programmable gate array) or an ASIC(application specific integrated circuit).

Processors suitable for the execution of a computer program include, byway of example, both general and special purpose microprocessors, andany one or more processors of any kind of digital computer. Generally, aprocessor will receive instructions and data from a read only memory ora random access memory or both. The essential elements of a computer area processor for performing instructions and one or more memory devicesfor storing instructions and data. Generally, a computer will alsoinclude, or be operatively coupled to receive data from or transfer datato, or both, one or more mass storage devices for storing data, e.g.,magnetic, magneto optical disks, or optical disks. However, a computerneed not have such devices. Computer readable media suitable for storingcomputer program instructions and data include all forms of nonvolatilememory, media and memory devices, including by way of examplesemiconductor memory devices, e.g., EPROM, EEPROM, and flash memorydevices. The processor and the memory can be supplemented by, orincorporated in, special purpose logic circuitry.

While this patent document contains many specifics, these should not beconstrued as limitations on the scope of any invention or of what may beclaimed, but rather as descriptions of features that may be specific toparticular embodiments of particular inventions. Certain features thatare described in this patent document in the context of separateembodiments can also be implemented in combination in a singleembodiment. Conversely, various features that are described in thecontext of a single embodiment can also be implemented in multipleembodiments separately or in any suitable subcombination. Moreover,although features may be described above as acting in certaincombinations and even initially claimed as such, one or more featuresfrom a claimed combination can in some cases be excised from thecombination, and the claimed combination may be directed to asubcombination or variation of a subcombination.

Similarly, while operations are depicted in the drawings in a particularorder, this should not be understood as requiring that such operationsbe performed in the particular order shown or in sequential order, orthat all illustrated operations be performed, to achieve desirableresults. Moreover, the separation of various system components in theembodiments described in this patent document should not be understoodas requiring such separation in all embodiments.

Only a few implementations and examples are described and otherimplementations, enhancements and variations can be made based on whatis described and illustrated in this patent document.

What is claimed is:
 1. An optical imaging system, comprising: amonocentric optical imaging module including one or more opticalelements having concentric surfaces to collect light and form an imageon a curved image surface; one or more curved and tapered opticalwaveguide bundles each comprising a plurality of optical waveguides thatare optically coupled to the monocentric optical imaging module atdifferent locations to receive different portions of the collected lightat the curved image surface, respectively, wherein each opticalwaveguide bundle includes an input optical waveguide bundle facet toreceive light from the curved image surface and an output opticalwaveguide facet to output light; one or more imaging sensors to receivelight from the one or more curved and tapered optical waveguide bundlesand to detect the received light, the one or more imaging sensorsconfigured to produce a representation of the image on the curved imagesurface of the monocentric optical imaging module; and a texturedsurface structure over the input optical waveguide facet associated withoptical waveguides of each curved and tapered optical waveguide bundleto enhance optical coupling from the curved imaging surface into theplurality of optical waveguides, wherein at least one of the one or morecurved and tapered optical waveguide bundles has a curved input facet,and principal rays of the monocentric optical imaging module input tothe plurality of optical waveguides are substantially aligned with anaxis of a corresponding optical waveguide to facilitate propagation oflight through each optical waveguide in producing a substantiallyuniform divergence of the light that is output from each of the one ormore curved and tapered optical waveguide bundles.
 2. The system as inclaim 1, wherein: the optical waveguides in each curved and taperedoptical waveguide bundle include first optical waveguide portions thatare bent at different bending angles, respectively, at the curved imagesurface of the monocentric optical imaging module.
 3. The system as inclaim 1, wherein: the textured surface structure includes a layer ofmicro prisms.
 4. The system as in claim 1, wherein the textured surfacestructure includes one or more of the following: a diffraction gratinglayer; a locally spatially varying optically patterned layer; a locallyspatially varying optically patterned reflective layer; a locallyspatially varying optically patterned refractive layer; or a locallyspatially varying optically patterned diffractive layer.
 5. The systemas in claim 1, wherein: each curved and tapered optical waveguide bundlehas a tapered exterior profile between the monocentric optical imagingmodule and a corresponding imaging sensor.
 6. The system as in claim 1,wherein: each curved and tapered optical waveguide bundle includes awaveguide section having a cross section in the tapered waveguide coreto decrease along a direction directed from the curved image surface tothe one or more imaging sensors.
 7. The system as in claim 1, wherein:the monocentric optical imaging module includes an optical aperture stopthat transmits a restricted portion of light incident on the monocentricimaging module at small incident angles to pass through the monocentricoptical imaging module while blocking light at large incident angles. 8.The system as in claim 1, wherein: the monocentric optical imagingmodule includes two or more lenses having concentric spherical surfaces.9. The system as in claim 1, comprising: an array of the curved andtapered optical waveguide bundles coupled to the curved imaging surfaceof the monocentric imaging module at different locations, each opticalwaveguide bundle of the array capturing a part of the image on thecurved imaging surface and different optical waveguide bundles capturingdifferent parts of the image on the curved imaging surface,respectively; an array of the imaging sensors respectively coupled tothe different optical waveguide bundles, one imaging sensor per opticalwaveguide bundle; and a microprocessor coupled to the imaging sensors tocombine individual images from the array of imaging sensors into asingle composite image representing the image on the curved imagingsurface of the monocentric imaging module.
 10. The system as in claim 9,wherein: the microprocessor is configured to reduce image blurringcaused by optical crosstalk of the guided light between adjacent opticalwaveguide bundles.